Defective is a strong word. It most likely works, lets just put it in. It looks like aluminum, so a steel screw should have no problem threading itself, if you can get it started.
Stick it facing up in the box with the Styrofoam. Get a hand held nut driver and push down really hard to start the screw. 'thread' all four holes while it's benched, and then go put it in.
If that fails, then it's 'defective' (because I'm not sure how you're supposed to thread a 1/2" deep hole with a tap where the cutting threads start a 1/4" up the shaft). And then we get another one at Trane's expense, until they send you one that's threaded (even if that's not how they come). A direct OEM replacement part should not have to be field modified.
If none of that is an option, my last resort would be to use an impact driver to drive my own (not fine thread) sheet metal screws in and call it done. Which is not ideal; something that shimmies that much should probably be fine thread.
Try their screws first, then give up and use whatever you have to.
The rest of this answer is wrong. The comments below it might help though.
What does the "other screw in the image" look like on the other end? If there's nuts, you take the nuts off, pull those ~8" long bolts out, then you can install it. Don't let it fall apart while you do it.
Usually replacement motors have these bolts going the other way, with studs sticking out that you put cap nuts on.
I think it's the wrong motor. When I google 2TTB0030A1000AA condenser fan motor, I get this: