It would've been 270 years since 1996 in "Space Seed" if Khan was found in 2266, not 200 years. But the year TOS was taking place in was problematic as it was being shot. It was taking place in nothing more specific than "the not all that far off" future. The "actual" years for events were nailed down, later.
We know it's 2259 in STID, so saying 300 year is certainly better than saying 200. I suppose if he'd said 250 that would've been better, but hey. And as DEWLine said, he could've been rounding back to his year of birth.
Edited to add: If Khan had said he was from 200 years ago like in "Space Seed", given it was 2259, it would've implied the writers retconned the Eugenics Wars beyond our time to the 2050s or 2060s (because they obviously didn't happen in 1996). That would've made some fans angry, and given them yet another reason to complain about the movie. So, he's from 300 years ago.