A garden gaming room is a different brief from a garden office even though it looks the same. What decides whether it works is latency, heat and light control: a wireless link that adds jitter, a small sealed room that a gaming machine warms by several degrees, and glare on a screen from a wall of glazing. All three are cheap to solve during the build and expensive to solve afterwards.
Run a cable while the trench is open
Wireless across a garden is fine for browsing and poor for anything latency sensitive, because the variability matters more than the average. A data cable laid in the same trench as the power, in its own duct and separated from the mains run, gives a stable connection for the life of the building. Doing it later means digging the garden up twice.
Plan for the heat the equipment makes
A gaming machine and two monitors put out real heat into a small, well insulated, airtight room. In winter that is a bonus and in summer it is unbearable. The answers are shading or solar control glass on the sunny side, a way to ventilate high up, and on a south facing room a small air source unit that cools as well as heats.
Light control is a design decision
Glare on a screen comes from bright surfaces behind and beside it. That argues for the glazing on the wall the screen faces away from, for blinds specified at build stage rather than bought later, and for artificial light that can be dimmed and aimed rather than a single bright fitting in the middle of the ceiling.
Power and protection
Several high draw devices, a monitor wall and a heater on one small consumer unit is a load worth sizing properly, and a sensitive setup at the end of a long run benefits from protection against surges. Sockets belong where the desk will be, at desk height, and there should be more of them than seems necessary.
Questions people ask about garden gaming room
Is wired networking really worth the trouble?
For competitive play, yes, and the reason is consistency rather than speed. A wireless link that averages well can still spike, and a spike is a lost round. While a trench is open the cost of adding a duct and a cable is small.
Will a garden room overheat with a gaming PC in it?
It can, easily. A small insulated volume plus a few hundred watts of equipment plus a sunny elevation is a warm room by mid afternoon. Solar control glazing and a means of ventilating are the cheap fixes and cooling is the reliable one.
Can I soundproof it?
Partly, and the useful target is stopping sound leaving rather than achieving a studio. Mass in the walls, a solid core door with proper seals, and avoiding a straight path from the room to a neighbour's window do most of the available work.