You know the diameter of the shaft from the other screw. Using that diameter or smaller, drill into the head until the head pops off. (Probably only about 1/8" deep) The rounded out head will keep the bit centered. If you do go too far, it will be into the bolt shaft, not the counter sink face. Remove leg and extract bolt with vice grips. If you drill past the head thickness and the head hasn't come off, re-drill with the next larger bit.
Tips:
Keep the drill bit in line with the bolt shaft.
Drill bit should be sharp and harder than the bolt/screw. Cheap drill bits rarely work well for this. If that's all you have, use the "step up" method mentioned below.
You do not need high rpms or a lot of pressure. Let the bit do the cutting.
For multiple fasteners, use drill lubricant to save your bit. With wood, just dip the tip of the bit into the lube so as not to have so much it stains the wood. Vaseline will work in a pinch.
When removing the remainder of the head from the drill bit, DO NOT grab it with your bare hands. It will be hot and possibly have very sharp edges.
Sometimes, especially for larger bolts, it is easier to start with a bit small enough to fit into the rounded out depression in the head to keep the hole centered. Drill deep enough to get into the shaft, and then go to a larger bit, stepping up until you get to the shaft diameter, which is when the head pops off.
I have done this numerous times removing "stripped" fasteners from aircraft panels.