Well that makes sense: the build script, for whatever reason, isn’t finding git in the path. But hugo doesn’t require git unless it is doing a git thing, like checking GitInfo.
I’m not sure what is included in the image at registry.gitlab.com/pages/hugo/hugo:0.55.6, but it looks like it’s about ~15MB, which I don’t think includes git. When I used a (self-hosted) GitLab CI build, I loaded a base Alpine image, and then installed git, hugo, etc.
On the other hand, you might be able to search gitlab.com and find Hugo deployment scripts similar to yours. 