Yup, you need either an Android or iOS device. If you just have a PC or a laptop you just can't use a Chromecast for some stupid reason.
At least it's better than Apple TV, which requires you to own a device from the exact same brand, but it's still a shitty requirement. They managed to implement setup from a PC before, what's stopping them from doing it again?
I suppose you could use any of the many Android emulators out there to get around this restriction but it shouldn't be necessary. This is just user hostile design.
You used to be able to set it up via any device though not just Android/iPhone which made sense as more than just phones can use it. At least it's not just Pixels or something.
https://support.google.com/chromecast/answer/2998456
"Download the Google Home app on your Chromecast-supported Android device."