Hey John,
Video player gets downloaded from your site (it’s included in the plugin), however video itself (the payload) flows through the WpStream cloud.
All in all, adding WpStream introduces negligible overhead to your WP hosting environment, so if could handle (e.g.) 500 viewers before it will handle that much after setting up video streaming.
You can find a short list of hosting recommends here
https://wpstream.net/forums/topic/hosting-servers/