Hello jlee51677,
Welcome to Apple Support Communities.
We understand you want to know if an Apple Watch that you set up for a family member can use apps for tracking times of a train, bus, etc.
Yes, they can use those kinds of apps. The article you came from should help you with setting up the Apple Watch for your family member.
"Put on the watch and turn it on
If the Apple Watch isn't new, erase it first.
Then put on the watch, or have your family member put it on. Press and hold the side button until you see the Apple logo."

Hold the watch near your iPhone
Hold the Apple Watch close to your iPhone. Wait until "Use your iPhone to set up this Apple Watch" appears on your iPhone, then tap Continue. If you don't see this message, open the Apple Watch app on your iPhone, tap All Watches, then tap Add Watch.
Tap Set Up for a Family Member, then tap Continue on the next screen."
More setup steps can be found in this article: Set up Apple Watch for a family member
Let us know if you have any questions.
Thank you for using Apple Support Communities.
Take care!