No. Programmers are no more a subculture than engineers, doctors, or lawyers. If professions were actually subcultures then the word wouldn't mean very much.
Let's look at the 6 criteria on the Wikipedia page:
1. through their often negative relations to work (as 'idle', 'parasitic', at play or at leisure, etc.);
This is obviously not the case. Most decent programmers work reasonably hard and enjoy it to some extent.
2. through their negative or ambivalent relation to class (since subcultures are not 'class-conscious' and don't conform to traditional class definitions);
Most programmers are middle-class, so this doesn't even really apply.
3. through their association with territory (the 'street', the 'hood, the club, etc.), rather than property;
Unless the internet counts as territory, I'd have to say no to this as well.
4. through their movement out of the home and into non-domestic forms of belonging (i.e. social groups other than the family);
A lot of programmers are on the anti-social side but again, and even the internet doesn't really apply here because everybody uses social networks now.
5. through their stylistic ties to excess and exaggeration (with some exceptions);
Most definitely not the case with programmers.
6. through their refusal of the banalities of ordinary life and massification.
Pretty much every programmer I know enjoys the casual comforts of beer, pizza, and computer games.
Verdict: No, programming isn't a subculture. It's a career. What you do for a living has very little to do with how your philosophy on society.