Damage Poppy is NOT DEAD!
Based on what Reign of Gaming has to say, Poppy will actually have some very strong Bonus AD ratios in her kit (max 140% on Q, max 100% on E, 90% on her ult) and playing her with some damage may actually be pretty effective at still being a bursty off-tank. Something like
+ boots would leave her very tanky while still having a lot of burst and damage.
Of course, she's not going to be one-shotting people like old school Poppy does, but she's not going to be some pansy CC bot either. A full burst rotation (W>E>Q>AA>R, assuming you aren't bad and actually land her Q and E's second procs) has max 1510 + 330% Bonus AD +100% AD +70% AP + 12% max health as raw damage. For comparison, her old burst rotation had max 800 + 200% AD + 120% AP, assuming you hit the damage cap on the % health damage (fun fact, new Poppy Q doesn't have a max damage cap anymore!). The big difference is that you don't get her ult's % damage amp, which brought her base burst rotation to a slightly more comparable amount at 1120 + 280% AD + 168% AP.
In fact, If you build her with the same style of AD and crit that is currently the norm for Poppy, she'll deal more damage than before by a lot, and she also won't be as weak early game. The only issue is she isn't so game-breakingly safe late game, and you have to have been living in your own little world if you expected her to keep that, since her ult and passive are the root cause of her rework to begin with.