To prevent this behavior, disable the Allow Screen Saver group policy at User Configuration / Administrative Templates / Windows Components / Windows Media Player / Playback.
The Allow Screen Saver explain text contains:
Enables a screen saver to interrupt playback.
This policy displays a screen saver during playback of digital media according to the options selected on the Screen Saver tab in the Display Properties dialog box in Control Panel. The Allow screen saver during playback check box on the Player tab in the Player is selected and is not available.
When this policy is disabled, a screen saver does not interrupt playback even if users have selected a screen saver. The Allow screen saver during playback check box is cleared and is not available.
When this policy is not configured, users can change the setting for the Allow screen saver during playback check box.