This morning I let my landlord know. It looks surprisingly stable, so he feels okay about not coming out to take care of it yet, but I'm watching it to be sure it stays put.
Looking at this more, I realize I was wrong in my first post about what happened. About half of one of the trees broke off in the wind. Looks like it first fell away from the building, then hit the next tree over and banged its away down to the ground, left leaning against the bottom half of itself, leaning back towards the building but blocked by the lower half of the trunk. At least that's what I think happened.
Means that this fell in a very lucky way. Holy crap. This could've been a lot worse. What if it had fallen towards the building? Or hadn't hit the other tree and gone toward the building just to the south of this one? Or had hit the cars in the parking lot (including mine)? Whoa.
Stay stable, large piece of wood.
I'll be in touch again with my landlord later.