... and so on. Correct?
If this is the case, does it matter if I trigger on the rising or falling edge?
Correct, with some caveats for real world circuits because electronics is not instantaneous:
o The data must be present and stable for a small amount of time before the clock edge, this is called setup time,
o The data must remain stable for a small amount of time after the clock edge, this is called hold time.
Violating the setup and hold times can cause very strange things to happen.
It does not matter which clock edge you use as long as you are consistent. It's common in real world computers to have multiple clock phases (same frequency, but offset from each other in time) so that setup and hold times can be honored.
Example: in the Hack computer the A register output is used to load the PC when jumps occur. Both these parts trigger on same clock edge, so there is possibility for insufficient hold time for the PC's data input.
Very common is to have a 2 phase clock
By using rising and falling edges of CLK1 and CLK2 you get 4 distinct times during the clock cycle when you can trigger synchronous logic.
I hope this is helpful, I expect that you may need to deal with setup time issues in your game environment.
PS: Actually this is for a game called Starbound. It is similar to Minecraft, but is a 2D sidescroller.
I'll have to check it out...