I think Abominations would be a suitable class for champions of League, but I don't agree with all your picks besides Urgot, Fiddlesticks, and Sion for that, which Sion of course would get Demon as well I am sure, with Fiddlesticks Phantom.
Since Teamfight Tactics is in Beta phase, anything can change, including Class types, or Class Comp Bonuses to balance the mode.
Chemtech's/ or "Toxic's," and Abomination's/ or "Mutation's:" (Class Comp Bonus TBD/ To Be Dediced)
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Property of, or belongs to Chemtech (Class type), for experimentation purposes, or assigned tasks, and this can work for Kog since Kog can be an acidic or toxic experiment of Chemtech, which Chemtech experiments can be unpredictable as well, but Kog' Maw Class Type can vary, as it doesn't have to be Chemtech, being that it looks like an Alien Creature pet...
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Causes Chemical or Toxin Hazardous damage of 5% of health every 3 (or 2) seconds, to "any adjacent enemy troops" near ally Chemtech Types. and by max Chemtech Bonus, it causes damage of 10% of health every 3 seconds to "all enemy troops" while max Chemtech is active. So if you enemy team's champion has 1100 to 1200 health, it will have done 330 dmg to 360 dmg (if maxed Chemtech, of 5 required) over 9 seconds time, which I feel is not too much. Also 750 health (at max Chemtech) would do 225 dmg over 9 seconds time. However, while at 750 health it would cause 114 dmg with the 5% dmg every 9 seconds time, or if every 2 seconds then 5% damage, then it does 190 dmg every 10 seconds time. Additionally, Chemtech's may also receive bonus dmg for Chemtech champions only, but only if it's not too much for the bonus overall...
Chemtech. Assassin
Chemtech, Wild
Chemtech (or Uknown, Abomination, Mutation, etc?), Wild
Chemtech, Abomination, Robot (Robotic/ Cyborg/ Cybernetic)
Chemtech, Abomination
- Granted Brief immunity and/ or invulnerability to certain damage, or spell damage, or all damage, with a duration, and overall function unknown yet, possibly able to health regen as well a certain (or "x") amount over a limited period of time (or depending on damage taken)...
Demon, Abomination
Phantom, Abomination
Abomination, Wild, Brawler/ or Mythical, Wild, Brawler
Mutation/ or Abomination
Abomination, Glacial, Wild
- Deals bonus 5% basic attack and 5% ability or spell damage "based on enemies health," being damaged by Mutations...
Mutation (or Unknown, etc?), Wild
Mutation
Mutation
Mutation
Mutation/ or Abomination
Mutation
Mythical's/ or just Mythic's (Egyption's/ LightStorm's/ Magical/ Mystical/ optional Class types, and Class Comp Bonus TBD)
- Can resurrect to auto Ult with a Random Mythic, then dies, but the ult still deals 25% (or so) less damage than when the champion is alive...
Mythical or Mythic
Mythical or Mythic
Mythical or Mythic/ Humanoid (Adapts well)
Mythical or Mythic
Mythical or Mythic/ Reptilian or Humanoid (Adapts well)
Mythical or Mythic
Mythical or Mythic
Mythical or Mythic

Intellectual's: (Class Comp Bonus TBD)
- Something to do with a Drone AI that provides for the allies according to negative affects on the champions, which would make for a great Meta counter because it can counter any negative affects caused to your champions (possibly removing a negative affect or preventing a negative affect that would otherwise have harmed the champion without the Drone AI Bonus), but definitely would have to be fair, so it likely should only occur for a duration throughout the match, for a period of time it lasts...
Intellectual
Intellectual, Assassin, Ninja or Blademaster
Intellectual or Crafter, Brawler, (Guardian?)
Intellectual, (Cybernetic, Cyborg, or Robotic, etc?)
Intellectual
Robot, Intellectual, Warper
Warper's/ Timezoner's or Timeshifter's/ Dimensional's/ Stunner's/ Paralysis or Paralyser's: (Class Comp Bonus TBD)
- Something to do with reversing time, or warping multiple champion allies with the class type as well, to provide a dodge to AOE based enemy champions when AOE's are fired off, making for a decent counter option, and maybe something else to go with this...
Warper

Psychic's/ or Telekinesis (But not Pychopaths and Class Comp Bonus TBD):
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Something perhaps to do with Zypher in the sense of how this functions, and maybe a Black-hole, or perhaps a random enemy champion turns on his own allies for a brief period with bonus stats applied to the manipulated enemy for a duration of time or until the enemy troop is dead, which the Tier level it manipulates or mind controls would be based on how many Psychic's are active in combat, which would go from Tier 1 to Tier 3, but Tier 3 would not gain bonus stats, and would last a shorter duration to balance this Bonus...
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or a Force blast that scatters all the champions positions, including the players own champions.
Psychic
Psychic

Nature's: (Class Comp Bonus TBD)
- Something to do with Vine Holds or a Nature Wall Barrier...
Nature, Sorcery
Nature, Sorcery
Nature, Brawler
Nature, Brawler, Phantom
Bloodmoon's/ or just Sorcery: (Class Comp Bonus TBD?)
- Something to do with health absorbing like a Vampire would do, which it takes health, but also gains some health from what it takes...
Bloodmoon/ or Sorcery
Bloodmoon/ or Sorcery
Bloodmoon/ or Sorcery
Bloodmoon, (Demon, Ranger already)
Bloodmoon, (Demon, Shapeshifter, Imperial already)
Warrior: (Class Comp Bonus TBD)
- Something to do with increased attack speeds, and more specifically dealing "bleed damage boosting" from basic attack strikes over time or an "x" amount from the start of combat...
Warrior, Blademaster, Sorcery (Riven wasn't exiled so I guess she wouldn't get Exile unless it's apart of her storyline?)

Phantom:
- At the start of combat, a champion's health is reduced to 100 hp... (already exists in the mode TFT)
Phantom, Demon, (Sorcery, Guardian, or neither)
Phantom, Sorcery, Brawler
Phantom, (Sorcery, Demon, or Guardian)
Phantom, Warrior or Blademaster
Unknown's: (Champ Comp Bonus TBD, perhaps a random effect mystery of a few options, if this becomes a Class Category)
Unknown, Wild
Unknown, Wild
Unknown, Brawler, (Guardian?)
Angelic's or Angels: (Class Comp Bonus TBD)
- Something to do with granting a Shield or Health boost upon death, to allies so that they can last a bit longer, also with a shield that functions like Kassiden but improves based on how many Angelic's active for the Class Comp, or a Percentage based on the Angelic champion's own health...
Angelic, Guardian, Brawler
Angelic, (Noble, Knight already)
(Angelic's or Angels/ Obliterator's/ Annihilator's/ Oblivion's/ Kings & Queens/ Odyssey's/ Absorbent's/ Alleviator's or Absolver's/ Perfectionists/ Acer's ----> "Random Odd" Class types for epic class names based on Class Comp Bonus Effects possible)
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Also we don't want so many classes that there's not enough variety within each class, so we don't want to have to many where it's not necessary to have a new class. So players have many options of champions within a class. There definitely has to be a fine balance on terms of how many classes may be apart of Teamfight Tactics, so it's not absurd either. As long as the classes we get, grant variety, and are overall truly useful to balance the game from a certain meta, then I think it's fine to have a new class in this case, but if it's nothing that's new enough with not much to offer that others can't already, then I feel it's important not use the class. I feel we want as minimal classes in TFT as possible (only where really necessary for the champions within), so that there's a great variety of champs within each class to build up on as the game expands its champions without breaking the game mode TFT.
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Many of these suggestions can mix well with Classes TFT already has, such as Void, Robot, Wild, Assassin, Sorcery, Exile, Knight, Brawler, or etc. Also Superhuman (or Supernatural), Zombie, and Alien were also Class types I was considering, but I don't think League has much or any of those, besides for skin types you can purchase with RP (Riot Points) to change the look to appear as such. Human or Warrior is also a class type I was considering!
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Each "Class Comp Bonus" should be uniquely effective overall in my opinion, and game balancing, both "meta counters" wise, and "aggression" wise, based on player's preferred play-style and roles to choose from. Some Class types are lacking, so perhaps Riot can consider this when they make future champions for League.
(I think Teamfight Tactics can be a great way for Riot to decide what their next Champion they can create should be, to introduce into League of Legends, based on particular Class types that League may be lacking...)