I think it was billed as 'scratch resistant' but I think that term is pretty hard to define. I believe it does have a scratch resistant coating, so it should scratch less easily than plastic without the coating, but it still is plastic in the end and plastic is pretty soft and scratch prone. It's clearly not going to come close to the scratch resistance of a smartphone with a glass screen.
I know I tend to be fairly hard on watches. I think all of my regular non smart watches have gotten some scratches over the years that I've worn them. The ones with plastic crystals fair worse than the better ones with glass or sapphire, but I've even managed to get a few small scratches in sapphire.
That said, I was quite concerned about how my pebble would fare, so I did get a screen protector right away. I actually did damage the first screen protector about three weeks after I put it on, so I'm glad it was there. I'd hate to see how the watch would look without it.
I do swim frequently (a few times a week) and I haven't noticed any issues with the screen protectors, but I haven't had one on for more than a couple of weeks too.