Donkey Kong 64 has a widescreen toggle in the options which I don't think you're using. This looks like 4:3 stretched to 16:9, you'll have a better time with real widescreen.
Rare were pretty good about this, after the first few games (Blast Corps, Diddy Kong Racing, Banjo-Kazooie?) they started putting widescreen support in most of their N64 releases.