Here's the thing: Getting your partner to police the time you spend gaming is not going to work.
1. Its YOUR responsibility to stick to whatever time frame you agree to.
2. It makes your partner feel like a nag.
This is a very, very good point. Being expected to police someone else's hobbies/responsibilities makes you feel like an exasperated parent, not a romantic partner, the same way having to repeatedly nag someone to do their chores does. Something like "Dinner in ten" called into the living room is one thing, but "Honey, it's time for dinner...... Dinner, now! No, now, not ten more minutes. I don't care if you're in the middle of a guild quest, dinner is ready - don't make me come in there." will really kill the romance.
One thing I will note - if someone has an intense hobby, whether it's gaming, or golf, or a club, or whatever, if they have kids, the hobby has to take a backseat for a long time. It doesn't necessarily mean dropping it completely, but things like 5 hour gaming sessions or a golfing weekend become rare, precious, and at the agreement of their partner only, because their partner is no longer free to amuse themselves while they do their hobby.
One of my gaming group has temporarily dropped out because his wife just had their second child. One of the other players is agitating for him to come back as soon as possible, and regards the wife as a bit of a control freak. I keep pointing out that they have two small children, the dad works full time, and his wife has followed him to a foreign country for his job, where she can't work even though finances are tight, has no local family, can't afford to visit family more than once a year, is left alone with the kids when her husband travels for work, and doesn't speak the local language. So yeah, spending a Saturday playing games should probably be shelved for a while.