Flash Player is going to use RAM. There's a balance between performance and speed, and there's some responsibility on the application developer to free resources so that we can garbage collect them. If the game continuously allocates objects and keeps them in use, we can't free those resources.
That said, it's also pretty common for complex games to consume a significant amount of RAM. Where the system doesn't haven RAM available, we're going to compromise performance to stay in the constrained memory footprint by aggressively purging texture caches and things. Garbage Collection is a CPU-intensive activity, which can cause the game to hitch, so we have heuristics that try to find opportune moments to do that. Rendering those textures is also CPU-intensive, which is why we cache them... so you can run in less memory, but then you have to keep making things over and over, which leans harder on the CPU.
As display sizes get bigger and more dense, it's also the case that those textures and caches grow proportionately as well. If you were to buy a comparable high-end 3D game from a commercial developer, you would see similar footprints, although there is overhead from running inside a virtual machine, inside a browser. Nothing comes for free.
In this instance, my guess is that the memory usage wouldn't be objectionable (and shouldn't have a negative impact on the machine), if you weren't encountering the performance issue.
For the performance issue, first things first, you should make sure that Hardware Acceleration is enabled in both Flash and Chrome, and that we're able to leverage it. There's a finite amount of GPU RAM available on your system, and we're going to fall back to software when that's exhausted. If you're running video streams, have a million tabs open and you're playing the game, that could easily exhaust the GPU resources, making them unavailable.
If you see good performance as the single, only open tab, and then you see a big degradation in performance as you add other content in new tabs (my guess is that the game will stay fine, but we'll fall back to software on some other new tab that we open) that's what you're seeing.
If you're seeing terrible performance on just the single, only tab, then it's time to a.) make sure you have the latest available drivers for your GPU installed, then take a look at chrome://gpu to see what Chrome is doing with your hardware. If the drivers for your hardware/OS combination are flaky, it's very likely that the Chrome team will have noticed in their aggregate stability telemetry and disabled one or more features on your GPU. Those features then become unavailable to us as a client of that browser. If the contents of chrome://gpu don't make sense to you, just copy and paste the contents of the whole page here. It should give me an idea about what's up.
So, long story short, the game developer is best positioned to deal with the memory footprint in this instance. We provide an excellent performance profiling tool called Adobe Scout, whichs allow them to identify what code is slow, and what code is consuming large amounts of memory. If they identify something at the language level that we're doing incorrectly, we have enough detail that there's an actionable problem to tackle; however, experience says that this is highly unlikely.
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