My DS2 (13 in a couple of weeks) goes to bed at 9:30-10 on weekdays during term-time, and has no fixed bedtime in the holidays. I set times if he seems tired, or play it by ear if he's occupied, happy and/or pleasant company.
I think the 5 minute warning was the problem in this particular situation, OP: 5 mins is not enough warning. For anything, not just gaming :) (tho' if they are mid-game, 5 mins won't get them to the end, and no-one likes to quit early). I know if someone gave me only 5 minutes warning to stop doing something I was enjoying, I wouldn't be happy!
I find advanced warnings work better: I'll remind him of bedtime earlier in the evening, then give a half-hour and ten minute warning. There's always usually a bit of grumbling and faffing, but never any major argument.
Bedtime does become tricky around this age, because they start to want to be up later than you do. Many teens do become naturally nocturnal (their sleep/melatonin cycles shift a few hours later into the night). This means there's an increased risk of rows if you're trying to get them into bed when you are already tired and grumpy! 
With DS1, I found I was depriving myself of sleep to get him to bed before me; 
and eventually I just had to give up and accept he was going to stay up later than me. This was around 14, as I remember. But certainly, with DS2 now, 13 feels too young, and I still want him in bed before I go... But I comfort myself with the thought that this phase will only last a year or so, at most. :)