Any Sim can do this but pair the Sim accomplishing this with the Playful, Lazy, Gamer or Nerd Trait for maximum efficiency here. This is really just a grinder like all the other skills but the benefit here is gaming is fun so your Sim will never want to stop!
First Step: Buy a Desk, a very comfy chair, and a computer. Unbreakable is preferred but if not, get 2 at least so when one breaks you can swap seats and have another Sim repair that computer.
Tips I'd suggest
-Steel Bladder is a must to maximize time
-DO NOT HAVE THIS SIM WORK. Unlock other skill builders that benefit from jobs you want this Sim to not be a functional member of Sim Society
-Buy 3 Gaming Books from the shelf and have your sim read those as you go for maximum efficiency (DO NOT DO THIS IF YOUR SIM IS LAZY)
-Having a second sim that cooks and cleans will lower the time your Sim needs to be bothered
-Lone Wolf Trait will lower the need to be social
-Enable emotional auras on FOCUSED items and stack it on the desk or around
-Always play SIMS FOREVER to start until bigger games unlock. Sims will never ever want to stop playing this.
-A radio near the computers also seems to help prolong gaming time