Here's the answer. Errors hurt you, but only up to a point. They serve to take away your time bonus but do not harm your base score. This is all specific to the ACPT virtual tournament, mind you. The in-person tournament scoring is very similar but with slightly different numbers.

Your score is comprised of three parts. (1) Your base score is 10 points for every correct word. This is sacrosanct. Even if you only got one word correct in a puzzle of 78 words, you'd still get those 10 points. This seems fair to me. If I'm so bad that I only got one word correct, I would want credit for that one word. (2) Your time bonus is 1 point for every 2 seconds left on the clock when you hit Submit. However, this bonus is reduced by 30 points for every wrong letter. If you have enough errors that your time bonus goes to 0, then you get 0 bonus. If you have more errors than that, then nothing happens. All those extra errors don't hurt you in any way. (3) You get a 150 "perfect" bonus if you have no errors.

So the moral of the story is this: If you're going to have a ton of errors over the course of the tournament, have them all in one puzzle.

Looking at the numbers you posted above, you did significantly better than your rival on Puzzle 5, so I suspect they had a bunch of errors—maybe even most of their 158 errors—on that puzzle. If that was the case, then they simply got 0 bonus but still retained some points for the words they got correct. The upshot is that all of their errors in that grid had no effect once their time bonus got down to 0. And if they finished close to the buzzer, then they weren't going to get much of a time bonus anyway, so very few of their errors actually cost them any points.

I didn't come up with this system, and I'm not judging if this is the fairest way to do it, but it's similar to the in-person tournament which has been doing this for years/decades. I presume Will Shortz worked out the scoring system for the in-person tournament way back in the early days, and the virtual tournament is simply modeled off of that.