Standard chess is much deeper than dipole chess for obvious reasons. No one meaninglessly moves knights and bishops around in chess - so that is not even part of the comparison. (If deeper means less variety - less turns as Joe mentioned.)
However, dipole chess could be interesting but the description here is very deceptive.
This is a pure 8x8 chess variant - it is by no means a slight change to the rules as suggested.
I would describe this honestly as follows:
A game with NEW pieces: THE PIECES ARE NOT THE SAME!!!!
the king ca only move one step forwards/one step diagonally forward. - it is not a standard chess king
Neither is the the very weak knight.
The bishop is not a real bishop either.
Nor the rook or queen.
And this 8x8 chess with 5 new pieces is very unlike standard chess even more so than large board 10x10/104 square variants with new pieces.
So in my opinion, this is not a modest chess variant but a complete makeover and change to chess. An 8x8 Fairy Chess just like any other Fairy Chess game.
I personally don't like using the term Fairy Chess - but it has been used for some time now to describe a chess-like game with new pieces.