Yes, although the watch is powered by DC, the LCD itself is driven by an AC signal that is generated by the electronics of the watch. Here's a little primer on LCD operation that may help explain it:http://www.displaytech-canada.com/pdf/ol_lcd/lcd_panel_LCDDesignCriteria.PDF
However, even if you do manage to build a suitable drive circut, there's another problem. That watch's display uses an elastomer connector, aka "Zebra Strip" (see page 6 of the above document), which can't be soldered.
Can it be done? Sure. Would it cheaper and easier to buy a more suitable display? You bet.
My advice is to take the battery out, throw it back in the drawer and many years from now you can impress your grandchildren with a rare antique.
Or bore them to tears. Either way works.