The Roku should work fine on a monitor.
Just go through that menu and say "the music did not stop playing" until it gets to the end of the list and throws up it hands and says "you can't control this TV with the remote."
Which you can't. That's the downside of using a monitor, no remote power or volume.
If the monitor does not have built in speakers or a speaker output, you will be limited to using remote audio on the Roku app or getting an HDMI audio extractor.