Don't know where the 2.5A is coming from????
The ~2.5A is coming from 300/120 - what he says the PSU is rated at
There's a few things of things that spring to mind over why the rating seems so high. As said above, efficiency isn't 100% at all - more like 80, perhaps less on a cheap PSU. So while you're getting 300W out of the PSU in useful power, it may be using another 50 (bit of an overestimate but the point stands!) in heat / circuitry / fans.
Secondly, it's possible that the PSU will be able to handle >300W for a brief period of time, such as on startup, when almost everything surges at once. So the 9A figure may well have been derived from this peak value rather than the continuous power rating.
And lastly, manufacturers always overestimate slightly rather than the other way round. If they think a supply will only ever pull 8A in normal use and they tell you to make sure it has capacity for 9, that gives a bit of a margin should the voltage drop slightly or something else untoward occurs. If they say it only requires 5 and therefore you put it on a 5A supply and it trips out constantly, they're going to have lots of complaints and potentially lawsuits on their hands!