obviously if the videos work great for everyone except for one person, the problem is not the videos. it sounds like the most likely problem is the route your partner's internet connection takes to get to your site. there's not a lot to do about that except have him change to another internet service provider. or perhaps other sites have unlimited and burstable lines on a bigger pipe?

why not have him do traceroutes at a couple times of day, plus pings from his computer to the site? then you'll have an idea of what's up.