Not, it’s a weird way to do it that is not quite there (as, you know, a lot of things). There is no winning score, other than doing the war goal - in the case of conquer, occupying all claims. Achieving partial goals (individual occupations) lowers the AI’s willingness to accept, or settle as things go, which you can track on the bottom part.
What attrition means, solely, although it affects AI willingness (although that might be because of resource and income loss), is that at after a while at 100% (you get a pop up) the other side can force a status quo; in this war goal, you swap whatever systems with claims) each side occupies - it’s easy to forget other systems don’t swap. Whether the trade is good or not is up to you.
If you’re not at 100%, you can keep going to smash the fleets or create more claims or whatever, though the AI will quickly concede when the “Achieve war goals” score gets to zero.