The original ATX designs used the PSU as part of the overall cooling system - they sucked in outside air, and blew it into the case. While the air was slightly hotter than ambient it was still better than not having it.
From the ATX spec
Adequate venting should be provided in the system to allow for
unimpeded and well-directed airflow to cool key components such as
the processor. One recommendation that is implicit in the ATX
specification is the placement of the power supply. The power supply
should be placed in close proximity to the processor if the power
supply is expected to cool the processor properly (but be sure to
observe the component height keepouts over the PC board). Chassis
venting should be placed strategically to allow for proper cooling of
other components such as peripherals and add-in cards. A system fan
should be considered to allow for proper cooling of all system
Modern gaming boxes tend to have significantly better cooling systems (and invariably have bottom mounted PSUs. and very large fans) - they don't rely on the PSU fan for cooling, and as such it makes sense not to have the PSU in proximity to the processor. You can still mount the bottom mounted PSU to blow air up (hot air rises, and the hot air will exaust through a top vent or fan), or down( PSU simply blows the air out, the other fans can handle cooling the rest of the system anyhow). I've got two relatively similar systems in an older top mount, and a modern bottom mount case, and the ambient temperatures on the modern case is about 2-3 degrees lower.
In most cases, with bigger cases, venting straight out the bottom makes sense, and is what seems to be recommended. Your rear case fan can handle additional processor hot air exhaust duties.
That said, keep in mind that some older PSUs have shorter cables that'll barely reach the motherboard on a modern gaming case - in my case I have it venting in cause its the only way I can use that darned old power supply.