There is a historical trend to add the possibility of orthogonal direction for diagonal draughts variants, and vice versa. For example, Armenian draughts added diagonal movement to Turkish draughts, Frisian draughts adds orthogonal direction of capture for traditionally diagonal western variants, etc.

This idea for this variant is quite straightforward: orthogonal direction of movement and capture is added to International Draughts (or any other variant), while maintaining the rest of the rules exactly the same:

-Men move only forwards, thus diagonally or orthogonally, and capture in any direction

-Kings move and capture in any direction

-All squares are used

This can be also considered as the simple adaptation of International Draughts to the full board.

It maintains one-on-one opposition (which is lost in most orthogonal and mixed variants), 2 kings vs 1 king and king vs man are trivial wins, king+man vs king is also a win in most cases but is trickier, etc.

In my opinion, when draughts were adapted from alquerque to the checkered board, using only the diagonal direction (and therefore only half of the squares) was a mean to prevent pieces to get stuck easily in the beginning of the game, since mandatory capture wasn't still a rule (“jeu plaisant de dames”).

Since then, draughts evolved producing great number of variants. I believe this is the next logical step in the evolution of this game, as several historic variants seems to forewarn. In fact I find quite surprising that this obvious idea hasn't been tried before.

I played a few games against other players and it seems to be well balanced. A  6x6 board is enough to make an interesting game. If someone is interested to give it  try, let me know.

Seems very similar to Armenian Checkers (TAMA) in my view.

https://www.boardgamegeek.com/boardgame/45755/armenian-checkers

There are some important differences: diagonal direction is only for movement, not for capture; and more importantly, there is not strictly forced progress, since men can move sideways, making the character of game extremely different (plus the added inconvenience that a lone king cannot force the capture of a lone man).

The idea behind the game is although very similar: expand the possibilities of Turkish draughts by adding diagonal movement.

Take this same idea applied to international draughts, and follow its consequences till the end, instead of stopping halfway: expand it orthogonally for both movement and capture. I don't know, I just find it perfectly logical, and even necessary, to proceed this way.