Precision is THE Marksman path, although AP/AS champions like Teemo and Kayle (maybe Azir?), can also have some benefits out of it, as well as some Melee DPS champions like Yi, Xin, and Udyr. Just like you're unlikely to see Marksman or Tanks taking Sorcery as their primary path, it won't be uncommon to see other classes avoiding precision.
Domination seems balanced between AP and AD, but is clearly geared towards Assassins, and I'd argue that it might be stronger on their AD variants simply because AD Assassins are in a better position overall.
Inspiration seems more of a "how can I abuse this shit?" path with worthy stuff for everyone. Glacial Augment is great for champions like Gnar who like to make sure they can land AA+Q+AA without giving anyone a chance to run away, and with only 2 secs of downtime, might be a decent substitute for champions who buy Frozen Mallet only for the slow. Despite that, it's also a great way to mid range mages such as Viktor to set up his combo with a slow into Death Ray.
The Contraption runes offer a secondary Flash, lane sustain, or a 600 Gold Reduction for Stoneplate, Zhonya's, or Guardian Angel by giving you a free component of those (the Stopwatch).
The Tomorrow runes offer either free boots, possibility to go in debt, or, as you mentioned, the extra damage to minions. The Minion Dematerializer works for both Auto Attacks and Abilities, so it shouldn't offer too much of a big difference between AD and AP champions.
Another point is that you seem to be grouping Precision and Domination as both being "AD".
Precision pretty much screams "Attack Speed champions only". You'll hardly ever see an AD Assassin or Juggernaut picking Precision as their primary path, as it favors glass cannons who can dish out sustained damage.
Domination is all about mobility and burst, so you won't see Marksman going for it unless they are going for an early game snowball (similar to doing a Lethality build on an ADC) and have not as much use to AS (for example, a Draven, a Lucian, or a Miss Fortune). You will see Assassins picking it, both AD and AP, as the burst it offers is bigger than the one offered by Sorcery, so it's hardly an AD only path.
While I'd hardly call the new runes balanced or say that they are a great addition to the game, I don't think they favor AD champions all that much in terms of options. You either are an AS reliant champion and pick Precision, or you are AD oriented and pick Domitation.
Tanks are the only ones who got pretty damn bad changes, as usual.
