Yes, rental cars and camper vans also need a valid Czech e-vignette. Usually Czech rentals do have a valid vignette arranged by the rental company, foreign renting companies most likely do not.
In order to avoid a heavy fine we suggest to make sure with the rental company upfront that the car has a valid e-vignette.
Vehicles with a maximum permissible weight of over 3.5 tonnes (incl. combo of vehicle + trailer) use a distance-based toll system (MYTO CZ) instead of the e-vignette.
Related articles:
What vehicles need a Czech e-vignette?
What happens if I drive without a Czech e-vignette?
Where can I buy the Czech e-vignette?
What is the MYTO distance based toll?
Where can I register for the MYTO CZ and get the on-board unit (OBU)?