Is the broken tool stuck in the stud?If not ,and the hole you drilled is bang on center,you can drill out most of the stud using a small bit,then a slightly bigger one,another bigger one,etc.Stop when you get to the threads,and collapse them inward with a punch.Lots of penetrating oil(I use ATF,works good)and a little heat will help.Finicky work,so take your time.If it all goes south on you,there's always helicoil,but the hole still has to be centered right,or the new stud won't line up with whatever part it goes with.The video shows the removal of a stud that was screwed in just before they shot it,yours has had years to seize up like in the real world.If it was in cast iron like most old cars,it would come out easy,not so with magnesium or aluminum.Good Luck!