Chromecast setup - not as easy as promised

Today, I bought a Google Chromecast for a friend of mine. The leaflet promises setup in three easy steps:

• connect to power and TV (via HDMI) => ok, no problem
• switch the source on your TV to the chromecast => ok, the splash screen asks you to open chromecast.com/setup to complete the setup
• open chromecast.com/setup => doesn't work at all - apparently, the chromecast fails to perform a DNS lookup for itself (sic!)

The only reliable way to get it to work seems to be to install the Google Home app and use that to setup the Chromecast - which is okay, but the leaflet and the Chromecast itself explicitly recommend doing it the other way. It's a shame that Google fails to provide correct information regarding such a basic thing.