Has ROVER ever thought about expanding to Europe, there is no such thing as a dog-sitting website?

There are such services in Europe. I stumbled across one called DogBuddy, which may have started in the UK, but also operates in many countries, including France, Spain, Italy, Germany, Sweden and Norway. In France, you can search for pet au pairs.

I Googled pet sitting Austria and came up with this company:

https://tiersitter24.at/en

and there were some other results.

Oddly enough, the "tiersitter" site looks somewhat like Rover's from a graphics standpoint.

As of Dec 2017 it doesn't appear like Rover is planning expansion or at least it hasn't announced it yet