A very interesting concept for the rules. Could you specify which game variant this applies to: 4x4, 6x6, or both? My question is based on the fact that the game board is variable and can double in size during the game from the initial 4x4 or 6x6 matrix. As I have already written in my posts in other threads, with the 4x4 board, I have only managed to collect all 14 cards against the AI in very few cases, when only the last two remained, which is 7 rounds. Most of the time, the game ends on average in the 5th or 6th round, sometimes even earlier. It also depends on the quality of the player.
If the rule about moving a column or row after each turn is understood this way, then I am interested in how many rounds the game ends on average with two players on a 4x4 board. In general, each game is very short.
When I first noticed the variant of a moving board after each move in your rules, I could imagine it on a 4x4 board, where a row or column would move after each move, but the size of the 4x4 board would remain unchanged. A card that left the 4x4 matrix after being moved would be inserted into the same row or column on the other side, so the 4x4 matrix would remain intact.
I'll try playing your variant with my girlfriend, but we'll need a bigger table for that :-)