The framing of this question is usually the problem. "They only play games" is said the way somebody might say "they only watch television", as a thing to be worked around rather than an interest to buy for.
Treated as an actual interest, with depth and specifics like any other, the gift list gets substantially better.
Find out what they actually play
Gaming is not a single hobby. Somebody who plays a competitive shooter with the same six people every evening has almost nothing in common with somebody who plays long single-player stories, and they want completely different things.
The way to find out is not to ask. Ask a teenager what they play and you get a name you will not retain and a wary expression.
Ask to watch for ten minutes. Sit down, say nothing, let them explain if they want to. You will learn what the game is, whether they play with friends or alone, whether they use a headset, how they sit, what their setup is missing.
The information is useful. The act of asking is worth considerably more, and quite a few teenagers have never been asked.
What is actually worth buying
The ordering here is deliberate. The first four are the highest-leverage objects in the room and the ones most teenagers are running the free version of.
A good headset
The single biggest upgrade available and the most commonly neglected. Most teenagers are using whatever came free. If they play with friends they are wearing one for hours a day, and a good one is a genuinely different experience rather than a slightly better one.
The chair
If they sit for several hours a day in a dining chair or on a bed, this matters more than any peripheral. A good office chair beats most things marketed as gaming chairs at the same price, and it is the one item on this list a physiotherapist would also recommend.
Whatever is obviously missing from the setup
A monitor arm, a second screen, a decent mouse mat, a light behind the screen so they are not staring at a bright rectangle in a dark room. Watching for ten minutes tells you which one, and the gap is usually glaring once you look for it.
A wired connection to where they actually sit
Deeply unromantic and disproportionately effective. Anything competitive is decided by latency, and a long ethernet cable or a pair of powerline adapters turns a bedroom at the far end of the house into a fair fight. Nobody asks for this and it is noticed within one evening.
A microphone, separately from the headset
If they talk to the same people every night, the thing five other households experience is their voice. A standalone microphone is the upgrade that improves the experience of everybody except the person receiving it, which is a strange and rather good property in a present.
More storage
Modern games are enormous and a teenager with a full drive is quietly deleting things they like to make room for things they want. An external drive removes a running annoyance they have almost certainly never mentioned.
A gift card for the platform they use
Unromantic and consistently correct, because releases move faster than gift buying and they know what they want. Give it alongside something rather than instead of something, so there is an object to open as well as a balance to spend.
A year of the subscription they already pay for
Not a new service. The one already coming out of their account, or yours, extended for a year. It is a real gift, it changes nothing about their habits, and it does not commit them to anything they will have to cancel.
The peripheral for their specific genre
A racing wheel, a fight stick, a drawing tablet if they build rather than play. High value if you have the genre right and dead weight if you do not, so this one depends entirely on having done the watching described above.
A second controller
Small, cheap and the only item here that changes who is in the room. A second controller is the difference between a solitary hobby and something a sibling, a parent or a friend can join without ceremony.
Merchandise from the specific game
High risk and high reward: exactly right is excellent, adjacent is worse than nothing. The test is whether you could name the game without checking. If you could not, this is the one to skip.
A game they are inside, rather than merchandise about games
The one category nothing else on this list covers, and the opposite of the merchandise gamble. For somebody who spends most of their free time inside games the format is completely ordinary, so being in one is not a novelty the way it would be for an adult who does not play. It is closer to being in a photograph.
What is not worth buying
A game you chose. Unless briefed precisely. The chance of getting it right is low and they will have to pretend.
Anything described as "for gamers" in general. Novelty mugs, LED signs, socks with controllers on. This is merchandise for the idea of gaming rather than for anything they care about, and it reads as somebody buying for a category.
A cheap version of a good thing. Cheap headsets, cheap chairs, cheap keyboards. They already have the free option and a bad paid one is not an upgrade.
Anything that implies the hobby is a problem. A book about screen time is not a present.
The one that works differently
There is a category of gift here that nothing else covers, which is a game about them.
For someone who spends a great deal of time in games, being inside one is not a novelty in the way it would be for a person who does not play. It is more like being in a photograph of a place you know well. The frame is familiar, so all the attention goes to the content, which is the people in it.
The brief that works is the same one that works at sixteen: make it about their friends and their references, not about them being young. A single-level build starting at £99 with the group as characters and the running joke in the level names is a very different object from something personalised with their name and age.
The friendship group is the point. A game they can send to five people who all appear in it gets opened five times on the first evening, which is the pattern described in what makes somebody open a game twice.
If you want to understand the interest
A small suggestion that is not a gift and is often worth more.
Most teenagers who play a lot have never had an adult take the hobby seriously enough to ask a real question about it. Not "is that not a bit violent", but "how does that actually work" or "what makes that one good".
If you want a way in, the technical side is genuinely interesting and it is a subject they may know more about than you, which is a good position to put a teenager in. Things like what makes a jump feel right or how a computer plays chess are the kind of thing that turns a shrug into a conversation.
What this means
Buy for the specific games, not for gaming.
Upgrade what they use for hours, not what they use occasionally.
And if you personalise it, personalise the friendships. That is the part of their world that a gift can actually reach.
