Just from the pictures, I suspect a little cleaning and corrosion removal would get that working. If you look under at the bottom of the cell holder, you will see some interesting "metal salts", if you carefully remove the screw to the left, clean all of that till it is shiny and replace the screw, then try it again, you my be rewarded with a working watch. It may in fact be the case that the left hand tab is simply missing, and replacing that with a piece of suitable thin plated brass or copper cut to size (from some other cheapo quartz) might get it working too.
Quite a number of the quartz movements I've acquired as "freebies" when purchasing other watches were similarly afflicted. A brass or fiberglass scratch pen, or even some fine grit emery paper will help remove the tarnish, be careful not to get any of the debris in the mechanism as even the tiniest particle of grit could prove fatal if it gets in the gears.
If you have a multimeter, then put it on resistance (or diode check) and briefly place one probe on the +ve tab and one on the -ve if you see no reaction, then you have a break somewhere, but if you get a high resistance, then you are probably making progress.
Bear in mind these things sip tiny amounts of current, somewhere in the order of 10μ A or less, so the resistance measurement likely to be correspondingly high. The coils blocks alone, are usually of the order of 1 kΩ to 10 kΩ. In other words, connecting your multimeter and expecting to see the current being drawn is a forlorn hope, unless you have a specialist meter that can measure in the μ A to p A range, but resistance measurement is an easier task.