In my humble opinion (and I could be wrong), they haven’t.
Let me explain. People who buy luxury watches don’t buy them for the sole purpose of knowing the time on their wrist. They buy watches because they like what the watch represents. Knowing the time is a ‘fun bonus’. People who wear a luxury watch won’t suddenly stop wearing their watch and trade it in for a Fitbit. Brands that should get scared are brands that sell watches in the same price point as most smartwatches. Mainly fashion watches, digital watches and cheap quartz watches feel the heat of the smartwatch industry.