Games are actually a complicated bit of software as they require several different resources not only from the system that you are using but also the people that write the software.
First and foremost, the game will only be as good as the people that write it.
If the programmers can't take full advantage of the hardware and optimize for it, then the game will suffer. This is why multiplatform games that are written once but compiled for different platforms suck.
Next, from the hardware point of few, games need specialized hardware, which is your video card. If you want to apply quantum computing towards a game, this is where it needs to happen(obviously for graphics). If you apply quantum computing to the cpu then you get things like more intelligent AI, more complex mapping etc, but it may or may not have as big of an impact.
But, the exciting thing about quantum computing is true SOC, where *everything* is handled by one core, which is great but limits upgradeability.