That's a poor way of wording it. "I use my abilities and they're not dead"
That would make you a burst mage. Swain was pushed in the right direction, gaining sustain to keep up trades. The issue is just that his Q requires him to be too close now and gets outtraded, keeping him relegated to a burst pattern of E - W - Passive - Q trade, and not enough tankiness to dps ratio to keep up in the midgame until like 5 items where he's almost too much to deal with alongside his team (but still not so dangerous alone). He's a teamfight mage with a safe enough laning phase that also enables ganks.
He is not at all bad after the changes, just a little less satisfying than what you would expect. Buffing his Q range back gave him the safety he needed, but as a battle mage, you might expect to be able to use the ability a bit more often and stick to targets, rather than be like an offshoot of Sion who offers CC and a bit of damage, but mainly exists as deterrent zone control and damage soaking.
A battle mages safety is usually inherently tied to their ability to keep up a skirmish and stick to the enemy or kite them, which Swain struggles to do and instead, has power elsewhere. It's still power, just... not what you would think a battle mage might entail until late game. I would honestly call him a control mage.
& 
because a large amount of the damage on it is simply the base damage.