A good place to start with gaming related gifts is, slightly obviously, with a game. Have you spotted the person you're buying for eyeing up the newest FIFA (always conveniently released before Christmas exactly for this purpose) or the new CAD. There are so many games to choose from, simply make sure you're getting them something they'll actually enjoy playing and don't already own by consulting their pre-existing game collection.
Another good place to start is with a decent pair of gaming headphones. How else are they supposed to chat away without them? An added benefit of course is that you don't have to listen to the video game if you're not into that. Some of the best headphones are the SteelSeries Arctis Nova Pro Wireless ones which are flexible and have swappable batteries, however these are quite expensive. The Astro Gaming A10 (Gen 2) however is much cheaper (though still not totally budget friendly), but it is one of the best options for those who don't want to go over the £50 mark. There are options for less you'll just have to do your research with those.
If you're looking for something a bit cheeper than this, maybe you have a £10 to £15 limit, then don't worry I've got you. If they play Sims then an expansion pack could be a fun, easy gift. Or perhaps something a bit more novel, a personalised pint glass that says 'gamers fuel' on (available on amazon) or a blanket for them to snuggle under or just to jazz up their gamers chair.
If the person you're buying for prefers boardgames and card games, maybe get them a travel version of one of their favourites. For example travel Monopoly or Cluedo are both pretty fun. Or just look into investing in a new board game. Some of my favourites are Chameleon, Articulate and Trivial Pursuits.
If you're really struggling just type 'gifts for gamers' into Google and I'm sure you'll find something perfect. Just don't forget that with gift giving it's the thought that counts more than anything.