I guess you should make sure that the PC is in good working order. Is Dune II the only game you're experiencing problems with? By testing a few other games you can check if your PC is running well.

Dune II is also a game with high conventional memory requirements. Especially when you turn on sound effects. I'd suggest you'd first start running the Dune II setup again and configure no sound and music nor mouse. Go basic and check if the problem still persists. If it doesn't disappear then check your Dune II installation or perhaps re-install it. If the problem goes away after configuring 'nothing' in the setup then I'd suggest you start configuring step-for-step. First no sound but with mouse support, then with both mouse and sound support.

Remember the memory requirements when you activate sound 😀. You can find a great deal of information on the web including on Vogons: Dos 6 conventional memory tricks .
Currently you have 569K conventional memory. If I remember correctly Dune II reports a minimum of 604K when everything is activated in the setup. It's usually not a big deal (once you know the tricks) to get up to 615K but it does need a bit of configuration.