The first is certainly valid reasoning in Go, and I phrased it in a way that should make that obvious.

I agree.

But you can also phrase it as "I've spent so much effort trying to reach goal X that I'm committed now", which is almost never sound in real life.

I think that this phrasing significantly changes the meaning of what you said originally, which was:

if I don't achieve goal X I've lost the game anyway, so I might as well continue trying even though it's looking unlikely.

I interpret this as assigning +infinity utilons to winning the game, and asserting that goal X must be achieved to accomplish that. I think it's completely valid, but the goal structure in life is so much more complicated than it is in go that it doesn't really transfer.

Your rewording sounds more like the sunk costs fallacy to me, but I think that it's terrible reasoning in go as well as life.

And on point 2:

I think there's an implicit "and I surely haven't made a mistake as disastrous as a two point loss" in there.

Which would make it valid reasoning. It might not be useful reasoning for life in general (as it's much harder to tell if you made a mistake than it is in go) but I think it's still valid.