No. Public transport in cities isn't included, except for journeys on the S-Bahn, and equivalent in some cities.
 

You'll need a separate ticket for the tram, or you could take the S-Bahn to Zürich Hardbrücke, and walk.

Correction: you could also take the S24 to Zürich Wipkingen station.

Some S-Bahn lines in Zürich are not included, only the trains operated by SBB or Thurbo.

If that's true, then Eurail need to specify on their website, because at the moment they advertise that it's valid on S-Bahn in all cities in Switzerland.

https://www.interrail.eu/en/plan-your-trip/tips-and-tricks/trains-europe/railway-companies