A buddy of mine bought a trade-in SIG P229 (dunno if it's a police trade-in or what), but apparently, it's got some kind of magazine-disconnect, i.e. it won't fire unless the magazine is in the gun.

Is there any way to remove that?

Is it just some addition to the "normal" P229, or is it a completely different fire control system?

Normal P229s, or other SIG Sauers, do not have magazine disconnects.  Some depts wanted mag disconnects, just like some depts wanted the SIG Pro 2009s with safeties.  If its a CPO(red box) I'd call SIG up and see if they will remove it, or if it can be removed.  Actually, I'd call them even if it isnt a CPO.

A common mistake with SIG Sauers is putting the trigger bar spring in backwards.  It may be that someone either at the factory or the previous owner did this.  It can make it feel like it has a trigger disconnect.  One end of the spring should go in a small hole left of the mag release on the right side of the gun, and the other end of the spring fit in a notch at the back of the trigger bar....NOT THE HOLE IN THE TRIGGER BAR.