GRBL is as said in Emgee's link a G code parser and machine controller that runs on many platforms including in this case an Arduino. This is the same basic functionality as for example Mach 3, but the latter has lots of additional bells and whistles such as wizards. It would take G code for example from F360 though you might need to find an appropriate "post processor" for this machine.
I think I would have two concerns about using it as supplied for your application. First, the feed seems to be by standard screws whereas your friend's CNC probably has ballscrews. This means that either you need to have backlash compensation (BC); or carefully generate your G code to only have unidirectional moves to a desired coordinate; or correct any backlash in the machine. From a quick look, there seems to be a BC option in GRBL but it may need a higher spec Arduino (Mega?) than this machine has. Now Mach 3 does have BC but in my experience though it works well if the basic backlash is small (my Novamill has about 0.01mm), but can't properly cope with the level seen on ordinary feedscrews (such as my Super 7 leadscrew). (Or it may be possible to get F360 to allow for backlash.) But you may need to at least fit low backlash nuts (e.g. using a plastic material moulded to the screw) or even ballscrews.
The other thing is that the version of this machine I looks at seems to use just a DC motor with a collet chuck attached as the spindle. This won't have wonderful bearings and may not run quite true, not so helpful if you are using small drills and want accurate positioning. You could upgrade the spindle of course.
It also looks a trifle dear – there are other similar machines that have a larger working area for similar or lower cost. Search eBay for "3020 CNC".