The Red Prince's game is a forced win, actually.
I'm not sure how the star-shaped board would effect how the game works, but I just assumed it was just a fancier rectangular board.
We're also going to ignore the fact that apparently players can make multiple moves per turn (The Red Prince complains about Ruby taking up his turn, after all), and that the pieces duel for capturing. Obviously if the pieces have to duel, then it's a forced win for red since I'm pretty sure the red pieces are always stronger than the white ones.
Another thing I'm just going to gloss over is that the pawns would just get stuck behind one another, and since the board is 8 tiles wide, that means, technically speaking, the most number of pawns you can get to the other side of the board is 8. So I'm gonna modify the rule to be "number of pawns stuck on the other side of the board."
Pawn games are usually either a forced win or extremely tedious. Hexapawn, the most famous example of pawn-only chess games is a forced win for the second player.
In fact, I will garuntee you that every chess game that's only pawns is either a forced win or a very tedious game with mindless trading of material until the last 15 moves, where zugzwang ideas finally appear.
Honestly, I'm glad it got turned into a fight scene, because there is so much wrong with the game.
The game starts off with a completely forced opening. Since there's only a two square gap between pawns, and the pawns can't defend each other because of how they move, the game will always be like this after 17 moves:
If you're wondering why it won't be the other "spike pattern," it's because this pattern maximizes the number of pawns closer to the centre, making it the best set of moves. However, even if the opening looks slightly different, it wouldn't matter because Black just immediately wins 8 pawns.
In the position shown above, it's White's turn. Notice how every legal move results in losing a pawn? This is what the board looks like on move 25
and as you've probably guess, this is what the board looks like after the 49th move
And this is where things get a big finnicky. Unless I'm mistaken, stalemate rules are never mentioned, meaning if Black captures White's last pawn here, it could just be a draw. But it's not like that matters anyway, since it's pretty obvious that the player with 28 passed pawns is going to win.
Obviously, since it's White to play here, if capturing all pieces means checkmate, then the whole game is an M50. If the stalemate scenario I mentioned above applies, then it's M54, since it will only take Black 4 more moves to push two pawns to the end of the board, and it doesn't take a genius to realize that 2>1.
So at this point, we just don't even know why players even try to play against The Red Prince. The forced win in 54 moves is obvious with all 54 moves being, well, forced for White. And you can't even blame the them for cheating since that's the only way to win as the first-moving player. The game's just a glorified version of Hexapawn.
Changing the pieces out for normal pawns does make it a bit better, but, also as I mentioned, that would just make the game needlessly boring with no strategy at all for the first 90% of the game.
Of cours, as I mentioned earlier, the star-shaped board could possibly have some effect on the game, but since we never actually properly see the wedges change something, along with the fact that the whole game is just pawns, the game would probably still be a forced win for red, anyway.