I'd say getting within 5 miles of a carrier constitutes stalking, wouldn't you?
My first CO on my first boat had a brass set. When you can read the names of the pilots and RIO’s on the planes landing on the Enterprise, you KNOW you’re close.
TOO close, in fact.
It's a question of intent. If I were a Chinese sub skipper who had stalked a U.S. carrier then the last thing I would do would be surface within site of the target and advertise my capabilities. I truly think that there is every likelyhood that Chinese skipper had no clue he was as close as he was.
You (and the author) assume that the USN was caught flatfooted by the bold, daring gesture of the gallant PLN, to which I call bull****.
Calling it "stalking" is on the order of saying that mice "stalk" snakes. Look, the mouse walks right up next to the snake! What a daring gesture by the mouse!