After many years during which I could not find a decent way to play this game without severe compatibility issues, I finally managed to do so by using the tool recommended by the user "Twilight" below (in his comment from March 2021). After installing said tool, I was able to run the game without any technical problems.
The in-game experience is almost identical to what it was 22 years ago (well, everything loads much faster now). I have successfully played both quick matches as well as custom games (including the campaign). However, the online mode doesn't appear to be working (which was to be expected), so you are stuck with local multiplayer if you want to play with your friends.
Note: Any match defaults to a very zoomed out view (as in, you get to see the entire map at once and the worms are very small). This can be altered at any time by zooming in and out with the mouse scroll. I am not sure whether this feature existed originally (I never tried to zoom in and out when playing on the small old CRT screens), but it is very nice to have it these days.
The game itself is, obviously, a more bare-bones version of Armageddon/World Party (less weapons, less customization etc.), but otherwise it plays just the same. I, for one, prefer this version due to its simplicity, but also thanks to its very cool soundtrack. In any case, if you've purchased this, you probably already know what to expect in this respect.
