Hmm... I don't know if the problem might be the browser version of itch.io. The Steam demo was released today, so you can try it there if you want; the game is exactly the same as in the videos!
Clicking the chest simply displays coins; there's no visual feedback when clicking, just coins.
Pressing "I" opens the inventory, where the swords are stored, and placing the swords on the altars activates the visual feedback (gold per second).