Not sure if cutscenes is the right word since the same issue applies to the opening crawl.
I tried using different compatibility modes but the changes were minimal, the animation of the Star Wars logo was a bit smoother on Windows xp service pack 3 but everything else is the same. Any way to fix it?

I don't understand: Dark Forces should run in DOSBox, therefore no compatibility mode should be needed.
Instead, I'd try changing the DOSBox output, setting it to OpenGL or DDraw: GOG provides a tool for configuring DOSBox, which should have been already installed with the game.
Otherwise you could try using DarkXL.

Thanks for the tip, I'll try setting it to DDraw.

All right it fixed the problem completely, thank you so much.