That is not the first observation that Gaming mode decrease total performance. And I have not found a good technical explanation what it really does. From general information, apart from disabling some "pop-ups" and background activity (which can improve performance if and only if these extra services are really running):
The goal behind Game Mode is consistency, rather than flat performance boosts (although it will bring some of that too).
Which can be an indication of some "real time" optimizations. Real time is always slower when compared by total throughput.
Interesting question how Sonar performs when asked to work in real time. The test can be as simple as putting the audio interface into fast settings (f.e. 96kHz / 64 samples in buffer) and then starting adding software effects till the system start "poping and cracking" periodically. Then switch into Game mode and test either it "pop/crack" more or less.
I mean it can happened that Gaming mode is not a bad idea during recording while a bad idea during mixing. But we all are able test it soon, so will see
The idea behind "real time" is that process get GUARANTEED amount of resources. This amount is usually lower then practical maximum the same process can get without guarantee. Also supporting such schema usually involve more process switching, which on common processors can reduce practical average performance during the same time slot. This "effect", while not technically exact, can be observed in Sonar when you switch the buffer from let say 64 samples to 1024 samples. The number of samples Sonar should process/produce per second does not change, but the load on the system is reduced while acceptable "jitter" in processing is increasing.