I played the original RE1 on, actually played like 3 different versions and if i recall correctly i had to press either F2 or F3 to access the "Settings" option to change different things like Resolution and keyboard. In GOG version i just can't seem to do this. I even tried modifying dxcfg.exe and still the Resolution stays the same.

Go to the game in your library and click the options button next to the play button. Under addition executables you can launch DirectX settings.

Use a proper ddraw wrapper, like dgvoodoo or ddrawcompat. You can select the resolution and much more, than in GOG's wrapper.

Right click on the game in the library, go to Additional executables, and click on DirectX settings.