It's quite an easy exhaust note to execute in some respects because, although it's raspy, it's quite a clean note - not unlike an E46 M3. It is missing the occasionally emergent 12 cylinder howl of the real car.
It sounds a lot like it could be from the same recording used to create samples used for other cars in previous games, at least I find it very familiar sounding (and being subtly distinct from the real car, as I already said).
This car has a very loud exhaust compared to its intake, so the lack of intake sound in the game is less apparent. Except for onboard, where an absence of lumpy modulation of the otherwise dry exhaust note is pretty clear.
The tone of the exhaust doesn't change off throttle in the game, because it's not how the sampling / synth scheme is set up.
There was only ever one car that had this feature in a GT game, the Subaru VIZIV Vision GT car in GT6, and even then only when it was first introduced, as they patched it out again. All the other cars had the same texture on and off throttle, albeit at a different volume, which itself resulted in extra effects on the other cars with AES-synthesised sound. But the VIZIV was always richer, until they patched it to be like all the others.
Patched version can be found
here.
It's best to try to match the volume of these videos when comparing.
The exhaust sound is basically almost silenced off-throttle in Sport.
These two issues continue to be GT's chink in the armour as far as sound is concerned: lack of dedicated intake sounds, and no proper on / off throttle variation for exhaust sounds.
Luckily, the McF1 GTR suffers less than most from the consequences of those design decisions.