I think part of the confusion may be that when the site was taken down, the mirrors that sprung up were things like goat.se, etc.
I’ve heard it pronounced “goatsee” and said that myself back when the original site was live. You are 100% right on the intent of the name though.
I feel like it had RPG elements with the soldier upgrades and equipment. There was progression in what your characters could do. This game was amazing, I’d love a remake of this with some small graphical and quality of life improvements.