Something like InfluxDB is a better thing to compare to TimescaleDB (and TimescaleDB does very well, though the benchmark was a bit old[1] and influx might have improved in the meantime).
Database types aside, what really gets me excited about Timescale is that it's just another Postgres extension. If you're already running a Postgres cluster for your OLTP workloads (web-app-y workloads) and have just a bit of fast-moving time series data (ex. logs, audit logs, event streams, etc), Timescale is only an extension away. You get the usual time-tested battle hardened Postgres, with all it's features and also support for your time series workloads. Yeah you could set up declarative partitioning yourself (it is a postgres feature after all) but why bother when Timescale has done the heavy lifting?
[EDIT] - see the response below -- the benchmark is up to date, and Timescale does even better against the purpose-built tool that is InfluxDB.
> Note: This study was originally published in August 2018, updated in June 2019 and last updated on 3 August 2020.
[0]: https://blog.timescale.com/blog/building-columnar-compressio...
[1]: https://blog.timescale.com/blog/timescaledb-vs-influxdb-for-...