I swear, it was the worst sound I've ever heard. The impact was so intense my passenger corner light popped out. So now there's a chunk missing from the sidewall. How bad is the damage? Do I need to get new tires?

 

In the situation that you describe, if it was me, I'd have the tire removed from the wheel and inspect both. Anything questionable about either one and I would replace it. I've bent wheels before where the tire still looked fine, and of course, I've had tires that needed to be trashed because the sidewall sustained too much damage (but the wheel was still fine).

 

The inner structure of the tire is much more important than the outside. A good tire is made to absorb a bad shock. But still, tires and brakes are the two things you shouldn't take chances on. A failure can be catastrophic.

I'd replace both tires on the same axle. You should do that on any car, but it can be escpecially important on an FD. If you rotate two tires with different tread depths to the back you'll find the Torsen LSD reacting in a funny way and the car will veer to the side when you accelerate strongly.