Marcin,
That clarifies things.
Exactly, your feature service is created automatically when you checked "Keep Latest"; I wanted to understand if you were referencing another feature layer that you created prior or not. You have your own enterprise database if you utilized "Create Enterprise Geodatabase" tool. In this case, you do not need ArcGIS Data Store.
Also, you do not need Portal for ArcGIS and ArcGIS Data Store to have feature service archiving from a Stream Service (especially for tutorials/testing). However, we typically recommend larger scaled configurations of ArcGIS Server, Portal for ArcGIS, and Spatiotemporal Big Data Store for Production utilization of GeoEvent.
I would go into ArcGIS Server Manager and delete your stream services/feature services and go back a few steps.
Try again and let me know if you experience the same issue.
Alex