just to correct your usage, "play" usually refers to a looseness in an interface that shouldn't have looseness. you have a very slight wobble.

it could be a few things. it's possible that your BB needs to be faced, like erichsia said. That means they take a special tool that removes the paint and a thin layer of the surface from each side of the BB, so that the BB can sit flush in the frame. But not having it would lead the BB to make poor contact. I don't think it could make the axle sit off center (since that would involve the threads) and lead to some crank wobble. If the BB wasn't installed by somebody who knows what they are doing, it could have been put in so that the axle is off center. If this is the case then your BB threads have been stripped.

Were the cranks installed by somebody who knows what they're doing? Maybe they are not tight.

Maybe the chainring is bent from shipping now. Remove the chainring, sit the cranks against a flat surface, and see if all of the chainring shelves sit flat. Lay the chainring down to see if it lies flat.

Then report back.