Setting the game to windowed mode fixes this issue, the problem is the only way to do this is in-game. Here's how to do it:

-Run RTC.exe (no parameters or compatibility required)

-Press your Print Screen key. For some reason this refreshes the screen so that you will be able to see it in black and white.

-From here, navigate your way into a game and then go into options and change the "Display Mode" to "Window". Press Print Screen after clicking to refresh the screen.

I hope this helped, if anyone needs more help feel free to ask.

DISCLAIMER: This worked for me, I have no idea if it will work for you.

Thank you. This solved my issue on Win7 64 bit laptop. It is a bit annoying but at least I can play the game in window mode.

Though, this fix works only regarding RCT Deluxe. RCT2 do not have window mode option ingame.

Does this work the same way on a Macbook Air?
Because I'm having the same issue :(

Only RCT3 was ever released for the Mac, and this solution is apparently for RCT1.

Try running the game in Boot Camp or a VirtualBox virtual machine of a Windows OS.