Hm interesting. Probably a bug. The game detects whether to use keyboard/mouse or to use buttons, maybe that code is broken on the first time you play the game. Will look into it! I tried it and it seems that the first time it does kind of force you to play on buttons, but on the second game session and third it works just like expected, so maybe if you exit the world and re-enter it will fix itself. Will be fixing that on the next update! Thank you for playing :)
Also if you're wondering how to do stuff, you can click on the spoiler that says "How to play with buttons". There you get a list of actions that you can do, like mining and stuff. You can only do one action at a time, though.
EDIT: oo, I just checked the code, to fix it temporarily you shouldn't just exit and re-enter the world... My mistake. You need to go to the settings and exit. I'll be patching the game now so don't worry.