It clearly DOES define what an air pistol is

it is an "Air Weapon" with a max of 6fpe which does
not have either a barrel length of 300mm OR an overall length of 600mm.
That is crystal clear because an "Air Pistol" over 6fpe is section 5 prohibited

,
and the quote you have put up clearly states that if it is over 6fpe but has EITHER a 300mm barrel OR is 600mm overall it is NOT prohibited
Therefore either a 300mm barrel or an overall 600mm makes it NOT an "Air Pistol"
Note the quote does
not use the term "Air Rifle" at all, it says "Air Pistol" or "Air Weapon other than a pistol" so those are the only two definitions that matter.
How can you not understand what is written in Queens English right in front of your face ???