While the same game, that won't exactly work, the stuff for your laptop and phone are separate and cant be installed on the other if that's what your asking.
Even if your laptop doesn't have a dedicated graphic card it is quite powerful, so you'll be able to play any popular PC game at least on medium setting. You can get lots of option from Steam. For a start, look at this list provided by Intel http://www.intel.com/support/graphics/sb/CS-034979.htm
I have an ultrabook with a Haswell Core i7, integrated graphics and 8 GB of RAM. It won't fly.
Although you can potentially get away with it, I've run games that failed (on another laptop), I wouldn't bet on it.
Well in Steam you could ask your friend for the game data backup and install it on your PC as long as you bought the game, you can't do that in Windows Store. Also now that Minecraft support Xbox multiplayer, invite me sometime to play