The bit at the start where the guy was going back and forth on whether to cut his own eye out also had me looking away too. I think I'm getting wimpier in my old age.
I'm not into those types of movies. Cube was different since it was more about the puzzle solving than the actual gore.
I hope the remake doesn't just go all out traps'n'gore and toss out the puzzle element.
Also - if it's a hit and they remake Hypercube - they surely will be able to improve on the original Cube 2. I prefer Sci Fi to Horror but that film was just BAD.
If the remake is successful and they do a sequel, I doubt they'll look to the original Cube sequels at all (I sure hope not). The thing I missed most from the sequels was the puzzley aspect of it. I do like to see a creative gory death when someone's time is up, but it's definitely not what draws me to the movie. I love the psychology between the characters, and slowly working out how the cube works. The sequels felt senseless to me in that regard.
Even though Saw and Saw 2 had a couple of wince inducing moments, they weren't what I'd call gore movies (maybe they ramp it up more in the other 50 Saw movies). The only such scene I recall from the first movie was the guy sawing off his own foot, and you only saw a bit of blood as he started, not giblets and stuff. The bit I mentioned in your quoted post had zero gore, it was the tease that he was going to do it that freaked me out (now that I know he doesn't do it, it wouldn't be bad to watch at all). Even though those few moments were unpleasant to watch, I don't feel like they were excessive or without purpose. I wouldn't be surprised if the later films focus more on the traps and gore though.