Anyone who plays 4IR on this website has probably noticed that red wins a large majority of the games played by top players. This seems quite strange to me (even though it happens in my own games), as yellow has a forced win in 7x6. If yellow folled the 7x6 winning algorithm in 8x8 ignoring the eighth column, would he get some kind of an advantage? Has anyone ever tried this?

no. the extra column allows red to win positions which would be lost on a 7x6 board by building a counter threat or under-mining a winning threat.