I have now updated to 8.1 and have updated all graphics drivers, and it does switch into fullscreen mode now.
A problem still occurs though: When I attempt to use a second monitor, the screen resolution is changed on the primary monitor and the engine is displayed in the top left corner of the secondary monitor.
I've selected the secondary monitor with the -mon command line option.

The fullscreen mode has worked properly on the secondary monitor before. At some point the engine froze and the fullscreen mode has refused to work properly ever since, even after several system reboots.
Any ideas?