If someone can find it, there is actually an official answer to this question out there.
Approximately 10-15 years ago, I was watching Die Hard on TV. I'm not sure which channel it was on, but my gut instinct is that it was a Turner channel (TBS or TNT). Anyway, whichever channel it was had shot a few brief interviews that they would air clips from during commercial breaks. After this scene aired, they played a clip which specifically addressed this question. The clip was essentially the scene from the movie with voice over narration.
Whoever was narrating the clip (I believe it was director John McTiernan, but I can't swear to it) claimed that in the original script, John was able to recognize Hans because everyone in the group wore the same watch. The narrator then claimed that he "decided to take that bit out and allow people to draw their own conclusions about how John figured it out."
Confirmed (and elaborated upon) here by the screenwriter, Steven E. de Sousza:
"Originally, [when Gruber and his men] get off the truck, the camera craned up, you saw them in a circle and Alan Rickman says, 'Synchronize your watches,'" de Souza explained.
"They all put their arms out in a circle with the camera moving down and they all had the same Tag Heuer watch. If you notice, the first guy Bruce kills almost by accident going down the steps, he searches the body, looks at the IDs."
Also in a longer cut of the scene, McClane begins to notice the terrorists' watches. "He steals the cigarettes, which is a laugh," de Souza continued. "He looks at the watch, which gets another laugh because you're thinking he might steal the watch. As he kills each guy, he notices they all had the same watch."
"When he talks to Dwayne Robinson, he says, 'I think these guys are professionals. Their IDs are too good. There's no labels on their clothes and they all have the same watch.'"...
"When Bruce [Willis] offers the cigarette to Alan Rickman, Bruce sees the watch. You see his eyes look at the watch. That's how he knows that he is one of the terrorists."....
However, the "synchronize your watches" bit was cut in the end because it came into conflict with the plan for the terrorists to escape in an ambulance, which was added towards the end of shooting.
Argyle (De'voreaux White) the limo driver crashes into the escape ambulance, but that ambulance was absent in the "synchronize" shot, thus leaving an even bigger potential gap.
De Souza added: "[Director] John [McTiernan] says to the editor, 'Get the scissors in there. Cut as soon as you can when they get off the truck so we don't see there's no ambulance.' Now without 'synchronize your watches,' all of these moments where Bruce looks at these guys' watches makes no sense."
- Esquire, The Screenwriter of Die Hard Finally Explained a Major Plot Hole; March 2, 2017