Go out with him and do things, introduce him to people that drag him out and do stuff with him. Get him to get a hobby other than gaming. Don't just say "talk to people", MAKE HIM talk to people.
The main obstacles for introverted people, that make them not talk to others, are:
Social Anxiety/fear
Is likely to apply to him to some degree
Mainly comprised of 3 things (although there can be more, in which case.. good luck):
- low self esteem. This one is nasty, but probably the most common reason why people don't start to go out and talk to others. I'm not saying that it applies to your brother, but if it does: Reassurance and validation over longer periods, coming from multiple people + him having the opportunity to prove to himself that he isn't low/weak/shit/whatever, can fix this one. It also is a natural byproduct from isolating oneself, so doing more with others will help in any case (if done right).
- not being used to talking to others. New things, or things you aren't used to/comfortable with, can be scary. Stick with him when he is in situation that he is not used to.
- being shitty at being social. Yeah, socially anxious people are shitty at being social. If he has this issue, make him understand that sociability is not purely a character-trait (seriously, who came up with this shit), but mostly a skill. He'll get better once he gets used to talking to people. It's all about getting past that first mountain.
Getting over the power of habit.
Most likely applies to him
Once you established a social network, being social is easy. Once you are used to going out 3 days a week, that is easy too. If you make staying home and playing games your habit, following that habit is easy. Breaking the habit is hard, but thats what has to be done to be social. So as I said before, FORCE HIM to go out and stick with him until he broke his power of habit, or get others to stick with him until he broke it. (This is easy to relate to as well, we all have our habits. Good or bad ones).
Related to that, there is also the the belief that "there is nothing to do" out there. This is because he only knows things that he does frequently. Tackle this by doing a wider range of outdoor-activities and habituating him to these.
Addictions.
might or might not apply to him
Mainly games, really. Break his PC, its for the greater good.- Running out of energy.
Probably does not apply to him.
Now this is the first thing on the list that is directly related to him being an introvert (it's also the only thing. Everything else is just correlated.)
Introverts run out of steam faster. I used to have this issue after 2 hours of socializing with a group. It caused me headaches, dizziness, I got really tired, moody and I couldn't think clearly anymore. Fixing this essentially means building stamina. Make him push himself every time he deals with other people. Take him to crowded places. Progress will show eventually.
However, the fewest people are so introverted that this factors in. Most people are just anxious, or can't get rid of their own habits and addictions that prevent them from going out.
Seriously, giving people advice that is intuitive anyways, is about the laziest way to "help" people. Most people know that intuitive stuff already, so I wouldn't even call it help in most cases. If you have the dedication to move in with him, you should at least go one step further than that, or two.
"EDIT: also how do I tell him that he snores and hogs the blanket at night without hurting his feelings"
If this hurts genuinely hurts his feelings, I fear the issue sits deeper.