I spent much more than 2h15m programming when I was a teenager (not every day, but I bet there were weekends where I hardly did anything else). Sometimes I programmed late into the night (my mom was pretty liberal about bed time, as long as school didn't suffer). There were also days I spent reading. Other kids spend equal amounts of time making music, or playing soccer. Turns out you become proficient at whatever you spend that much time on.
2 hours a day doesn't strike me as a whole lot. Even 3 hours seem okay if most of that time is spent doing something productive. That leaves the larger part of the day for other things, so I wouldn't worry. Make sure that he doesn't use his screen time just to play video games -- becoming proficient at video games doesn't really seem like a worthy goal to pursue -- and that he doesn't neglect his social life (meaning meeting friends in person). Programming can make you lonely because it's so stimulating for the mind you want to keep doing it, but you can't really talk to anybody about what you're doing because to outsiders it just sounds boring to hear you explain how you solved a certain problem they can't even begin to understand. It's also a nice activity to pursue if you don't have a social life in the first place - the computer acts as a substitute to get a positive self-image from (hey, my program works! I'm so good!). So watch out for that.
Maybe make a deal with him that his screen time includes watching TV, so he can use it either for programming or for watching TV.
As to studies to back up my contention that screen time isn't harmful in itself, a recent study seems to agree with me.
And a disclaimer of sorts: StackExchange is loaded with people with a programming background. So you might not get the same answers here that you might from other people.