[LONG POST] I've seen people ask if Riot controls the meta, so I thought I'd make a post about it.
But before I give my opinion on it, let's answer exactly what a meta or metagame means in terms of a competitive game. The term "metagame" usually refers to the most efficient way to play the game if one is solely aiming to perform the best. Metagame can also refer to a player using knowledge not immediately available to their character to change the way their character plays, typically in order to enhance their performance in the game. Also, I've seen meta commonly be an acronym for "Most Efficient Tactics Available" or some similar variation.
So how does this refer to League of Legends? Well, the knowledge not immediately given to a player can refer to which champions are the best given a certain patch. This external knowledge can be found by the professional or high level players of the game and is not evident whatsoever if you just look at the numbers/characters of the game. Another example of this is the lane setup of the game; when first playing the game nobody could figure out that a 1-1-2 jungle set up was the best way to play the game. That information was found from an external source: the high level playerbase.
So now answering what a meta or metagame is in regards to League of Legends, does Riot control the metagame of League of Legends? In my opinion the answer is yes to an extent. Yes because of the champions they choose to continually buff/nerf. By this I mean more specifically, they control the meta by buffing certain champions to a point where they aren't optional to pick anymore, thus dictating the Most Efficient Tactics Available.
By looking through the patch history of LoLwiki, a few obvious examples can be seen. Let's take Tristana for example. Keep in mind that Patch 1.0.0.152 was the preseason 3 patch in which every character received a buff to their movement speed. At this point Tristana wasn't exactly a top tier champion due to characters like Ezreal and Corki dominating the game; according to Riot she was a balanced champion. Fast forward to Season 4 worlds and she's one of if not the best champion in the game. Here is tristana's patch history from the end of season 2 to late season 4.
V4.10: Draw a Bead - The bonus range is now applied to Buster Shot.png Buster Shot. Rocket Jump - Mana cost reduced to 60 at all ranks from 80, Now more accurately checks for nearby landing spots when jumping close to, or over, walls. Buster Shot - Base range reduced to 550 from 700, Spell range calculation changed from 'center to center' of Tristana and her target's champion hitboxes to 'edge to edge' of the hitboxes.
V4.5: Stats Base armor increased to 19 from 15.
V4.4: Rapid Fire - Cost reduced to 0 from 50.
V3.03: Attack speed per level increased to 4% from 3.01%.
V3.01: Rapid Fire - Mana cost reduced to 50 from 80. Explosive Shot - Damage increased to 110/150/190/230/270 from 110/140/170/200/230.
As you can see, these are MASSIVE buffs for a champion that Riot considered balanced at the end of season 2. Now arguing whether she was strong or not before the buffs is debatable but the fact of the matter is these massive combined with the infinity edge buffs did cause tristana to be a mandatory pick in competitive play. In that sense, because players were forced to pick her to win, yes, Riot did enforce the meta.
Another example of this is Annie. Ever since the end of Season 1 she was considered lackluster. Riot noticed that she wasn't being picked so here's what happened next.
V3.8:
Summon: Tibbers Tibbers' health increased to 1200/2100/3000 from 1200/1600/2000. Tibbers' magic resist increased to 30/50/70 from 25/45/65. Mana cost reduced to 100 at all ranks from 125/175/225.
V1.0.0.154:
Disintegrate Mana cost reduced to 60/65/70/75/80 from 60/70/80/90/100.
Incinerate Targeting cone is now attached to Annie.
Molten Shield Cooldown reduced to 10 seconds from 16. Duration reduced to 5 seconds from 8.
V1.0.0.152:
Stats Base movement speed increased to 335 from 310.
V1.0.0.141:
Summon Tibbers Reactivating the ability while TibbersSquare.png Tibbers is active now allows you to control your pet, similar to Alt+Right Clicking. You will also see a self-only targeting particle when using this ability, depicting what command your pet is following.
V1.0.0.139:
Base health increased to 460 from 424. Incinerate Mana cost reduced to 70/80/90/100/110 from 80/95/110/125/140. Molten Shield Fixed a bug where it was returning damage to turrets. Duration reduced to 8 seconds from 15. Cooldown reduced to 16 seconds from 30. Mana cost reduced to 20 from 25. Armor and magic resist bonus increased to 20/30/40/50/60 from 10/20/30/40/50.
V1.0.0.138:
Pyromania - Now works like other charged passives; activating a spell with the stun no longer builds a charge, but the number of charges required to energize reduced to 4 from 5.
Yea, I think we can say she was buffed to the point of being mandatory. And that's exactly what happened next. Support Annie pretty much was forced down the throats of top players because Riot overbuffed her to the point where if you didn't pick Annie you had a much harder time winning. Again, Riot in a sense DID enforce the meta because they buffed Annie to the point where she became the best pick: i.e. the Most Efficient Tactic Available.
There's a ton of other examples of this too: Syndra being another obvious one if you look at her patch history, Gangplank being another one (in season 1 Riot buffed him so much that they nerfed him every other patch to tone him down). However, the funny thing is this trend isn't only with champions. Items fall under this category as well. A huge example of this is how dominant spellvamp was in Late Season 1 and Early/Mid Season 2. When Hextech Gunblade came out the stats on it were abysmal, then afterwards EVERY stat on it was massively buffed to the point where you'd see gunblade built every game, oftentimes more than 1 due to the fact that they were stackable. Will of the Ancients dictated the top lane meta for months due to how efficient it was. In a sense, by Riot buffing Wota to such insane levels they DID enforce the meta because the best choice because to run double AP compositions and having both build Wota, giving 50% spellvamp. After months Wota was nerfed.
Rabadon's Deathcap was another huge example of this. Season 1 Worlds was dominated by douple AP comps because Deathcap was so overpowered at the time (155 AP and 30% Bonus for 3300 gold). The power of deathcap forced teams to use double mages because that simply was the best way to win at the time. Deathcap was nerfed after Season 1 worlds.
Tl;DR, Riot in a way does enforce the meta because oftentimes they buff champions/items so hard that they become must picks/bans in top play, thus enforcing the metagame because by NOT using those champions/items the top teams have a much lower chance of winning.