No, you're not being unreasonable at all. It is always a process to learn how to live together, and there can be a lot of immaturity in that situation even at the age of 26. But the balance is all wrong here, and it sounds to me like you feel like you're his roommate because that's exactly how he is treating you. He is either consciously not prioritising the relationship, or simply doesn't understand your (quite reasonable and normal) needs. Either way, he's acting more like a child than an adult. I agree with the poster above. You need to make it very clear to him that this is making you unhappy, and that things need to change. And that, in reality, that must mean him spending less time gaming. It doesn't mean he can't have a hobby. But it sounds like he's basically spending as much time on it now as if it were a part (or full) time job, and that is too much if he also wants to be in a relationship with you. If he doesn't respond positively to that, I think you should leave him.
Ultimately your needs aren't being met and you need to be with someone who can meet those needs. And think of it this way. You're at the early stages of living together. What happens when you both get busier with work? When you get married? Have kids? Due to work and child commitments my wife and I generally have a window of about two hours in the evening when we can relax, and it's often less than that. In that time we have to decide whether to spend time together, to do things individually, or (more often than we'd like) to tick some chores off the to do list, tidy the house etc. I spent quite a lot of time playing computer games in the past, but spending more than about two hours a week gaming is unusual now. It's obviously not like that for everyone, but when your commitments increase, and especially if you have children, do you think he can reach a point where he can prioritise you and them over his gaming? Because if he doesn't, your life will be onerous and miserable, and you will utterly resent him. You must have a partner who can properly support you can meet your needs, whether you want to have children or not. It very much sounds like he can't at the moment, and unless that changes, I think breaking up with him is positively the right thing to do. Simply put, you deserve better.