"What size makes it a woman's, a man's, or a unisex watch?"
There is nothing anywhere written in stone...these are subjective classifications. The terms are not set by a governing body of horologists, the terms are strictly marketing strategies!
Look, barring any feminine decoration or overt design (pastel pink straps, roses or cute kittens painted on the dial, filagree cases with lots of gems and pearls) if the watch is too small for a man, then it is a woman's watch. If it's too big for a lady to wear, it is a man's watch. GENERALLY SPEAKING, if the watch is under 32mm, it's a ladies watch, but even this definition has been fading in the past 6 or 7 years where female executives have taken to wearing decidedly "male-sized" watches. The men's watch genre isn't helping either: When I joined WTF, men's watches were being introduced at 40mm...today, a 56mm Invicta barely raises an eybrow!
What it all boils down to is: if you like it and want to wear it, knock your socks off - nobody else is going to care one way or the other. If it bothers you sell it, or stick it in the back of your sock drawer, and buy a big manly macho watch. As I type this, I'm wearing my 32mm Omega Seamaster DeVille. I wear it everywhere. God cursed me with slender wrists, and this seamaster fits my wrist PERFECTLY! And I wear 1948-to-1960 Hamiltons that are even 2mm SMALLER. I don't care. I wear what pleases ME!
BTW you may have noticed I use millimeters when I speak of watch sizes. That is the industry standard, so you had the wrong tape measure for this job. We measure the watch from side-to-side alond the narrowest axis: for your watch, the line would start at a spot between the 8 and nine and extend ACROSS THE CENTER OF THE DIAL to a sspot between the 2 and 3. Your watch appears to measure 31.25mm which would be considered in today's unwoke world either a "unisex, or a large ladies" watch. I would consider it simply a handsome Timex. I lean towards Hamiltons and Gruens, but I could easily see that watch in my own wrist. Enjoy!