If you google “dress watch definition” you will get a bunch of links to forum posts of people arguing over the definition. It’s seems like there is no fashion consensus.
It seems the only etiquette that can be agreed on is that you shouldn’t be wearing a watch at all to a black-tie event.
So, with no over-arching definition, let me present mine. In my humble opinion a dress watch should be something actually worn with dress clothes. A suit, a jacket, or at least a tie.
The actual watch should be very flat, under 40 mm in diameter, on a leather strap, and have no complications. No date windows, or power reserves, or anything else extemporaneous. It should slip under your sleeve and appear discreet.
I think those are the requirements but for myself I’d also prefer it was an automatic and had a sapphire crystal. That’s because I would consider a dress watch a potential heirloom piece. But that’s no reason to begrudge someone buying a cheap nice looking quartz because they just need something to wear to an event.
Here’s an example of something I wouldn’t consider a dress watch but is one of the first results from an Amazon search:
photo Amazon.com
It’s on a steel bracelet, has a chronograph complication, and is too big at 45 mm.
This in my opinion is a much more relevant “dress” watch returned by Amazon’s search:
In my eye, that’s a more elegant looking timepiece.
These are just my opinions. Figuring out what a dress watch should be when I first got into watches and was first attempting to dress well. Hopefully my definitions gives some guidance if you needed a starting place.
The last thing I have say on this is – If something looks good on you, it looks good on you.
Becoming An Old Man 
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