My best guess then is his account is bugged. I have a friend who apparently can never get the SP challenger achievement. I forget the exact details, but it was something about a disconnect during the last boss fight. Whatever happened, apparently something triggered the server to think she completed the achievements she should’ve earned then but without actually awarding them to her (vet and speed run iirc). Because the server thinks she already has them, even if she beats it on vet or on vet in under the timer limit, she doesn’t get the achievements. And customer support has said there’s nothing they can do re: account-specific bugged achievements.
If he’s had any connection issues during the Domihaus fight in the past, it could unfortunately be the case that he should’ve earned the speedrun that time but didn’t for similar reasons, and now never can.
If I remember to I can see if I can get the speedrun later today on a character who doesn’t have it yet. If others can’t then it’s probably a bug with the global achievement and something ZoS could fix, but idk how or when they could’ve broken it considering I don’t think Falkreath has been touched for several patches now (BRF was around the launch of Summerset, however).