I suspect it would be more successful to redirect your gaming urge than try to make a reward for deprivation. Example: I enjoy reading and fell out of the habit for a long time due to spending all my time gaming so I made a conscious effort to include a goal of reading for a period of time daily (20 mins or 1 chapter was where I started, with the option to keep going).
You also could try journaling. When you have those bad feelings or ‘I wanna game’ write down how you’re feeling in the moment. Could also include writing yourself a reminder of how much better you feel when not in the throes of game withdrawal.
For me, I have been able to set boundaries to keep my gaming within limits that I feel good about. I play a couple hours in the evenings, I have a log-off time that’s early enough for me to read, socialize, veg out with my spouse (he’s also a gamer). I play most of the day on weekends because my husband is also happy gaming most of the day on weekends. Those kinds of boundaries may work for you at some point; so perhaps framing it more like a hiatus or a break will make the initial change easier to stomach.