Simply put (according to the Anandtech Article) Game Mode comes down to the following:
automatically for Games from the Windows Store) are run at a higher priority compared not only to system processes but also to other user processes (like updaters which not only Windows but also GeForce Experience, Keyboard Software, etc. tend to run). So when both the game and another application have work ready for the CPU it's more likely that the game will get it (while so far all user processes had the same priority and that meant that the OS would try to be as fair as possible (which could mean that the updater would run instead of the game).
- Threads belonging to Games will have CPU affinity. This means that even if context switching occurs the game threads will resume on the same core, meaning that it will in all likelihood find most of the required data still in the cache. If it were not for the affinity setting it might resume on another core and first have to go to a higher level cache or the main memory (which takes longer).
So in that regard I can understand how game mode could help mitigate slowdowns in both UWP and Win32 games. It obviously depends on how taxed your system is anyway and how much other software is running. If the game you use only uses 4 cores and you have a 6 core machine this likely won't have much if any impact at all.
Actually this highlights a topic of UWP vs Win 32 Apps (not games) where UWP is quite an improvement. Win32 Applications run or they don't. If it's badly written it can tax your CPU at basically any time it wants to. This isn't true of UWP Apps. When they get sent to the background they get limited time to finish what they're doing before the OS freezes them completely (or even removes them from memory) - unless they belong to a limited set of categories that can retain some kind of background capability (e.g. Music playback).
All in all my take is that as described this has the potential to benefit issues like stuttering due to the system being busy with something else. When it comes to higher framerate absolute numbers however I highly doubt any impact on Win32 games in exclusive mode and likely even in UWP games.