Yes, the 6x7 board is a first player win. I used to think that applied to the 8x8 board as well, and discussed the matter with grade1teacher, who thought otherwise. However, I have now joined the consensus that I discovered exists among the top players here: black has the advantage on the 8x8 board. The extra column negates much of 6x7 theory, and so far I can see no win for white.