I personally like shadow effect. It does make it hover, but the flatness still remains. I have used shadow effect with inset shadow to give button more roundness on the edges.
https://jsfiddle.net/kd1sbwnn/3/
Update: Thanks for all your advices and help! Have made the slight change as shown below. Once the user taps a tile, a small description is displayed. Does this look any better?!
What I would have in mind:
- Minimize clicks/taps that user has to do for navigation
- Pictures can be more descriptive than a words
I don't like that mobile version where user needs to tap twice to navigate (tap once - description appears and tap second time to navigate).
I recommend for the mobile version to add a picture and a button name.
Maybe something like this: https://jsfiddle.net/kd1sbwnn/7/