I once looked into this and there's actually more than a handful of theme parks like this, one of which even has a few locations:
The diggers don't move, they're fixed in position, and don't rotate, but otherwise you have full control of the arm using the normal stick-type controls.
My 4yo daughter picked it up far quicker than myself despite me being a life-long gamer, but we all had a fantastic time.
There are various games set up with different type of "diggers" such as "hook a duck"; with a hook on the end of the arm, 10-pin bowling; with a mini wrecking ball on the end of the arm, tyre stacking, where you drive a weird looking machine with pincers and rear wheel steering (that one was challenging) and of course "dig a hole".
Ever better is hiring a mini-digger from your local plant hire company when you’ve got some real work to do