I don't really care about the anime breaking the game's rules.
I mean, I hate the anime for a lot of reasons, but this criticism honestly seems just... wrong to me. Why does this bother people? The anime isn't the games, and the translation to a visual story-driven (... pft) medium should include it's own set of rules. Yeah, Pikachu beat Onix with it's electric moves which it can't do in the game... so what? I could understand if the criticism here was about it not promoting finding alternate strategies, but targeting it just not being possible in the games seems kinda dumb. I want to see the Anime do something different from the games, otherwise why would I watch it? Do we need to have it be turn-based and have every character on a square-based grid map? I like seeing Ash's Pokémon pull off shit they couldn't do in the games, that's like the only good thing about the series!
I don't mind them finding alternate ways to use a move. Battles in the anime are not turn based, 3 dimensional action. Of course there's going to differences in the way they battle and I like seeing that. Though my problem is when they either changes a moves effect or do something that doesn't make sense for that move to do.
Changing a moves effect: Aqua Ring heals some HP every turn (which I guess in battle would mean it'll either constantly be slowly healing or every so often would get a small heal). But yet Skyla's Swanna was able to heal its Burn status with it. Now you can make the argument that it sort of makes sense, but the problem is that's not what the move does. They're not using a move in a unique way or combining it with another move, they changed the moves effect therefore making it not the move they said it was anymore. Worst yet Swanna can have the Hydration Ability (it's Hidden but Skyla's a Gym Leader, she can have a special Swanna) so it could have just used Rain Dance and have its Ability heal it.
Move use that doesn't make sense: Thunder Armor. You all saw this coming. So how can Pikachu summoning a lighting bolt down on itself and Swellow for a little while create an energy aura made of lightning around them that can cut through all attacks sent at them? I don't even know what they could have done alternatively (other than the writers not writing themselves in that situation). Maybe had Pikachu stand up front using Spark while Swellow did an Aerial Ace thus creating an Electric Shield strong enough to block special attacks as Swellow gets in attacking range?
A good example: Counter Shield. I don't want to be all negative so how about a good example of the anime doing something unique? The Counter Shield was basically a Pokemon firing off a special attack while spinning around. What this did was make the attack also spin around and can be manipulated to surround the user this acting as a makeshift shield. That's okay, that's using the anime's advantage of having fast action battles. We also got to see plenty of variation of Counter Shields, sometimes even used by Ash's opponents.
Another good example would be when in Sinnoh a Pokemon would eat one of its attacks and gain a power boost. They only did it a few times, but was an interesting idea. What would happen if a Grass-type at an Energy Ball or an Ice-type ate an Ice-type attack? It's something that can't be done in the games and even in the anime it was an odd situation that created surprising results for everyone watching.
Though one final complaint is that I do get annoyed when they don't focus on the right thing about that Pokemon. And I'm not talking about a Pokemon using a Special move when its a Physical fighter, in the anime an attack is an attack (and defending against an attack is defending against an attack). What I'm talking about it a lot of times they say a Pokemon is fast to show how powerful it is when infact that Pokemon has a low Speed stat or what they should be focusing on is its high attack, defense, ability to learn a special move or have a special ability, etc..
EVs and IVs: Hmm, maybe they should make it so that if you increase a certain EV enough it'll increase an IV.