Is it mandatory to download TAG Heuer Golf on my mobile if I use it on my connected watch?

To use TAG Heuer Golf on your connected watch, you first need to download the app on your mobile and then link the account to your watch. https://faq.tagheuer.com/articles/en_US/FAQ/How-can-I-pair-my-TAG-Heuer-Connected-to-my-TAG-Heuer-Golf-account

You also need a network connection (either via your phone or via Wi-Fi) to download courses. The watch will then be able to function in total autonomy.