When the game is in the main menu, the mouse cursor is visible and highlights the 3rd or 4th option.
As long as the mouse hovers this option, you can't use the "Up" & "Down"-keys to select another menu option.
The mouse blocks the input. You have to move the mouse cursor aside to use the keyboard keys.

Please correct that in the next version and please add a Linux version ;)

That's not a bug. The game just uses the mouse for menu navigation when the cursor is highlighting something. Once you move it to the side you can use your keyboard keys. The game simply supports different ways of menu navigation.

If that's by design, i can only say that a "clean" Navigation Method should switch forth and back between both, depending on what the user wants to use and not depending on where the mouse cursor actually is.
The solution could be that If the user uses the keyboard, the mouse cursor could be hidden until the mouse is being moved again.

From a developers point of view that's just a bad excuse (in MY opinion). I can't remember any game where one input method blocks the other. They all switch instantaniously.