Is it a must to implement a physical system to get the colliding and interacting discrete grid movements?

I’m new to unity. I have to build a game similar to “Phylo” @ http://phylo.cs.mcgill.ca/. Please point out some way or related tutorials.

No, it is not. Actually the implementation of that game is rather bad. Just grabbing one of the tiles often shifts neighboring tiles you don’t want to shift.

I won’t search for tutorials for you as this is not a place to drop search requests. You should be able to use google the same way we are able to. Also don’t expect to find a tutorial for every possible game concept. Tutorials are ment to teach basics concepts which you should be able to transfer to other problems. When you search for “Unity shift puzzle” you should find several examples and ideas how to implement such a game.

However the exact behaviour you want is something thats a specific problem / goal you set for yourself. If you’re new to game development you may want to start with an actual specification of your game mechanics. You should be clear about want you want before you try to solve it. Write a game design document first.

Only use physics calculations if extreme necessary. You can use trigger events to simulate it.