Mine Shaft was a genre localized on Puzzle Picnic back when the site was still live. I can't seem to find it anywhere else, though I wouldn't be surprised if it's appeared multiple times and I never realized. Mine Shaft is really a Snake variant of sorts; IMO "Hydra" would be an appropriate name for it. I actually think it's superior to Snake in some ways. While the less-restrictive structure of the solution means you generally need more clues to make puzzles unique, it also allows for more localized progress in areas, and I think there's more you can do with it overall.
Rules: Shade some cells in the grid to form a "mine shaft" -- that is, an orthogonally connected group of cells which contains no loops (not even 2×2s) and does not touch itself diagonally. Given circles indicate all cells which are adjacent to exactly one other shaded cell. Numbers above and next to the grid indicate the number of shaded cells in the corresponding row or column.