This is a pretty unspecific question, so an unspecific answer is that fuses are a safety device that cuts current off if the powered device pulls too much current.
This could protect an electrical or electronic device from causing a fire if it malfunctions due to overheating or a short in the wiring. Many devices have fuses in them even though you don't know it. I suspect that computer power supplies do, monitors do, etc.
An arcade cabinet is a mess of power sucking devices and potentially a rats nest of wiring. Real arcade cabinets often have a fairly open monitor with line current pretty much exposed. ANd they go into environments where they could suffer a lot of abuse. So for a real arcade cabinet, some extra protection is needed.
For a homebuilt, it depends. If you just have a computer, computer monitor and low voltage wiring (controls) with good ventalation, it is unlikely that you need to be overly concerned. But it wouldn't be a bad extra safety feature. If you have line voltage exposed due to an arcade monitor, bezel lighting, etc, then a fuse becomes more important.