Does anyone know a way to make the original roller coaster tycoon run in a 16:9 resolution (e.g 1280p x 720p) on windows 8.1?

Did you try using Hex Editor? Follow this instructions:
http://www.wsgf.org/dr/rollercoaster-tycoon
I can only confirm that it worked nicely for me but I have Win 7

I just used the in-game settings to switch to windowed mode, and I double clicked on the window title area, and it maximized the window to my widescreen laptop display! The game now looks much smoother (not pixelated) and it's really widescreen!! Just awesome!! (I did not modify the game in any way, I use plain vanilla GOG RCT, as installed, that I recently bought).

Use the 'Borderless Gaming' freeware FORK by mdbell: https://github.com/mdbell/Borderless-Gaming/releases to get borderless and fullscreen, though the game map does not scroll when the mouse is at the display borders, but that's really not an issue, since we can scroll the map with the right mouse button.

Use 'X-Mouse Button Control': https://www.highrez.co.uk/downloads/xmousebuttoncontrol.htm - to easily map the mouse wheel and buttons to what you please. I mapped my mouse whell to PageUP and PageDown, and set these keys in the game to zoom in and out, respectively, and now I have mouse controlled zooming! I also mapped my mouse wheel (button) press to HOME and use that to rotate the game map.