The G860 essentially has the HD2000 graphics chipset, however it is a slight bit slower in clockspeed.
It will certainly handle minecraft fine.
And CS:GO will be playable at a mix of minimum/medium graphics. (30-40fps)
It is by no means a powerhouse, but it should tie you over for the time being.
It basically has the Intel HD "1000". It is slow, but at least it is a little better than their old GMA 4500. So while the Intel HD "1000" is crappy, it is not as crappy as their older graphic tech.