Yes, though that building does use some concrete and steel: https://matadornetwork.com/read/wood-hotel-sweden/

> The hotel’s not without any metal, though. Generators and heating/cooling units on the fifth and sixth floors are supported by a steel truss. There’s also concrete atop the hotel to minimize sway. But for the most part, the Wood Hotel is a marvel of white wood and forest aromas, like living in a life-sized doll house designed for the 2020s.

Obviously much, much less than a typical tall building though.