Ok, spent 22 years in the USAR and deployed, so I've seen military watches, and them that sell some.
Just for a baseline, a real military watch is spring powered, with fairly large luminous numeric characters on the dial. Subdued low light colors, and a OD woven band laced thru both springbars.
You can go from Timex and Casio $25 models, up thru some pretty high end version for that. The actual soldier isn't usually issued one, it's a special MOS type thing - SF, Dive, Command, SEAL.
Since they're 100% tax dollar, price is important. In the day, Timex, Hamilton etc. Now, Marathon, or CWC. <--- Those are issue. The ones listed are for sale to anybody. Not anybody buys them, tho.
A watch a soldier buys is usually something he can rely on, will take a beating, and is affordable. At the groundpounder level, Timex, Casio, G-Shock. In the day, Seiko Dive watches were the discerning choice. They were actually sold in the PX in Vietnam, durable, and now actually iconic from the era among private purchase.
The MTM, Chase Durer, really, not so much. It's somewhat other that what the public thinks, soldiers tend to shy away from the uber tactical stuff. It's a matter of not staying in your lane. If you aren't actually SF/Delta/SEAL, then wearing one is a bit poser. The culture is hierarchal in a way, and more than bluntly honest. Covert OPs warriors don't wear Overt Special Operations Watches. Kind of a dead giveaway, except for the SEALS. They wear RESCO, because it's made by a SEAL, for SEALs. That's honest. But, they don't really look like a high end tacticool watch, either. All duty, no bling.
If it's got a NSN and CAGE number on it, it's much more likely to be a true military watch. "Black OPs" needs deniability, a SKX007 with no country of origin does the job better. You can't trace the wearer back to anything as long as he keeps his mouth shut.
Just my opinion having been in.