Yes, buses and coaches up to 3.5 tonnes need an e-vignette if being used on Slovak toll roads.
Vehicles that exceed 3.5 tonnes of permissible weight use the distance-based toll system (MYTO) instead of the e-vignette.
Related articles:
What is the MYTO distance based toll?
What vehicles must use the MYTO?
Where can I register for the MYTO and get the on-board unit (OBU)?
What are the penalties for MYTO violations?