I fucked up by stripping this laptop screw, and wanted to drill the head off by drilling from the center of the screw to the side, but I guess that requires me to go around it, damaging the plastic way more. How can I get this out still?
Try the rubber band trick. Alternatively get a screw extractor.
Ideally, you'd be able to cut a new slot into the head with a small rotary cutter (read: a Dremel) so you can get some torque to unscrew it (and you'd use a different screwdriver too so you don't strip the slot you just made).
It looks too stripped from that pic for the rubberband trick.
A screw extractor might work, don't have one, haven't used one, so I dunno.
The "Captain Hindsight" solution, BTW, is when you start to strip it, you take one of the screws that's already out to a decent tool store, and you try it against every screwdriver in the store until you find the one that fits it perfectly, and then you buy that screwdriver.
When the screwdriver and laptop are united, you use it with a decent amount of downward pressure to turn the screw, carefully, *clockwise*. Because you started to ruin the screw turning it anticlockwise, the clockwise mating surfaces on the head aren't ruined yet. Once you feel it turn, that means the thread has unbound, and you can carefully screw it out.
As to your predicament, a dremel with a cutting ball should enable you to cut the head into a flathead without damaging anything visible from the surface. Use the smallest ball you own and go slow and careful.