With a lot of trial and error, and a bit of patience, I reached "the end" of the game. Quite a nice little adventure after all.
Some starting hints for future players (spoiler alert):
- Find the pickaxe first just outside the mountain, then equip it by pressing 1
- You can now dig earth tiles left or right of the player by clicking on them
- You can also dig down and up, but when clicking you also need to hold W or S accordingly
- Dig out all gems and bring each of them (by using E) to the "bench" outside the mine to unlock the next phase...
With a bit of polish, this could be a fun game. Enjoyed it!