In order to get the tamed Gatcha to drop loot crystals make sure you have owl pellets and stone in its inventory. 1 owl pellet + 20 stone per loot crystal. If you have tamed snow owls just park them near the gatcha and the gatcha will pick up the pellets automatically.
Gachas are essentially living lootboxes and resource farms. They will eat anything (including stone, wood, or fiber) and turb it into crystals which can drop a variety of resources including black Pearl's, organic polymer, or obsidian, among other things. They also have a rare chance to drop higher-tier crystals which turn into upgraded armor and tools