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The problem of the slippery king - the king that can keep evading your
attacks - has 'probably' existed since the beginnings of chess. It
becomes very evident in higher dimensional chess, 4D being enough to
require some drastic measures, and 3D mates are not a cakewalk. We likely
fail to recognize how difficult mate is even in FIDE. Even there, special
assistance is required, in the form of a small board with straight edges.
Consider how difficult it would be to mate a bare king on an infinite
board. Minimum force needed would be a K, Q, and N vs a lone k. 
K _ _ _ _
Q _ _ _ _
_ k _ _ _
_ _ _ _ _ 
_ _ _ N _ . . . And how do you get to that position? I would suspect at
least one more piece was required.

Going to 3D makes the problem more interesting. Using standard 2D FIDE
pieces extrapolated to 3D lets the king move to 26 cells in a 3x3x3 cube.
This is a good bit harder to cover, even with 3D queens. David Paulowich
made the point that there was no demonstration of minimum required force
for bare king checkmate in Raumschach not all that long ago. Has the
situation changed?

Going to 4D just explodes the problem. Even limited 4D like Hyperchess
gives far too many ways to escape to make mate practical without some
specific rule(s) for that purpose. That is, unless you make the pieces so
powerful the king cannot escape, which brings its own set of problems, but
does allow easy checkmate. Ben Reiniger's TessChess, using all the
higher-D diagonals for movement, is an excellent piece of work exploring
this area. Without question, king and queen can mate bare king. I don't
know about other piece combinations, but he has done beautiful
extrapolations of the standard FIDE pieces to higher dimensions. 

And I, with excellent help, am happy to report that the minimum requirement
to force mate in Hyperchess is demonstrated to be any 2 'major' pieces
and king vs bare king [the major pieces in this specific case being queen
and bishop.] For a very simple, linear approach to 4D chess, this is
actually a good result. It's nice to know that, after years of effort,
your game is not only playable but winnable. Well, I think it's playable.
And it is the easiest 4D chess game that gives you both chess and 4D, by a
lot. :) Further, there are probably 5 or 10 people in the world who agree
with me. Lol, it's still a good game. May all 6 of you enjoy it!