At least domination is fully compatible with Arena. You can use all the cards and special tiles from it in Arena, and you can use everything from Arena in Domination. Heck, you could even use the V'Tar orbs in Arena without them being a win condition. It would however benefit from it's own forum section because the strategies used in both playing and building your spellbook are very different.
Academy is a totally different game with some major differences in rules and is not compatible with anything from the Arena sets (barring house rules). It 100% needs it's own forum sections.
Academy is too different from Arena to count as an alternate variant, but it's not different enough to quite count as a completely different game.
Personally I think it would make more sense to divide the Mage Wars section of the forums into Arena and Academy, then have a sub-forum for each battlegrounds set under Arena. Remember that Domination isn't going to be the only battlegrounds set. There will presumably be more in the future, such as Archmage.
Well, it would make more sense if Academy's playerbase wasn't almost nonexistent. If Academy had an entire section of the forums devoted to it I'm guessing barely anyone would read it most of the time.
I wonder if there will ever be battlegrounds sets specifically for Academy. It would be cool to have some official Academy variants.