Warlords grant bonuses to his allies. The Bravura Warlord penalizes enemies by granting attacks and CA to his allies. When you do that to yourself, it's pure damage. If all your attacks deal pure damage, you are leaning to striker.
Several fighter powers lean themselves to damage. Including the fighter powers that grant extra damage based on weapon choice. Brute strike: Pure damage. Frost Backlash: Pure damage (and it happens when someone attacks you, to boot!). Reaping Strike, Cleave, Reckless Strike, Burning Blade, Flame Cyclone, Corrosive Ruin, Crushing Blow, Armor Piercing Thrust, and that's just within the first tier.
The fighter also
pushes/slides enemies. Footloose Lure, Tide of Iron, etc. There's no difference between 'you attack them, and push them' and 'you push them, and attack them'.
Also, the RD's powers aren't all
pure damage. I was asked 'what does the RD when it gets someone to come engage it'. When the RD has been engaged, they have done that defender part (get the enemy to come to me). I have discussed earlier in this thread what those defender powers would constitute: bringing the enemy closer. For instance, if I had added a status effect to 'Bleeding Barrage', you'd have called it a controller instead of a striker.
I could easily argue that the Swordmage is all damage. He's doing all kinds of damage all over the place. He has area affects which are just 'pure damage'. That he's too much a striker or a controller, by your standards.