Is it possible to install CyanogenMod for "Samsung GS4" on a "Samsung GS4 Active" device? As I was desperately waiting for the 4.4 update on my Samsung Galaxy S4 Active, I read that Cyanogenmod was available for the Samsung Galaxy S4.

My problem is: Is it possible to install the CyanogenMod ROM for the Samsung Galaxy S4 (GT-I9205) on my Samsung Galaxy S4 Active (GT-I9295)?

NB: The GT-I9295 is more or less the same as the GT-I9205, but has physical buttons. So I assumed that the drivers (and the ROM) could be different, but I'm new to Android ROM hacking.
This is actually an important question, and far better to ask now than try it and be stuck with a blank screen!
Android ROMs are specific to the device. This is why CyanogenMod and others have the specific device model and code name on them.
Even in cases where the deveice looks and feels the same and has the same name e.g. Samsung Galaxy S4:

GT-I9505
GT-I9500

They both run Android 4.4 now, and they look and to all user purposes are the same device. Under the hood there are differences, and no ROM will be compatible between the two.
I had used the Google Edition S4 as my example as ROMS weren't compatible between two devices with EXACTLY the same hardware, but work arounds are being found. The general rule is: If your device isn't specifically listed do not install the ROM!
In your case here I'm sure it will brick the device as there is different hardware (buttons etc), a different model code, and a different partition structure.