SUCCESS!!!! I connected my new Roku Streambar to my computer monitor (Dell 27 4K UHD Monitor - S2721QS). No extra cords or cables needed, other than those that came with the Streambar and the Dell monitor. No weird adapters or anything needed! No issues with the HDMI port on my computer monitor NOT being HMDI-ARC -- the sound simply plays through the Streambar, and the computer monitor shows the picture (i.e. Netflix show). And the picture quality is great, just as I expected with this screen purchase. I now we double use out of the screen, as it is my home office monitor by day and guest room TV by night. Hope this helps someone because I looked high and low for answers on this and couldn't find a solid answer! Roku customer support actually told me it wouldn't work either and that they dont advise weird adapters or anything as they arent tested. BUT I DID IT WITH NO ISSUE!
Things to consider: My monitor has an HDMI connection port, my monitor is 4k UHD screen quality, and my monitor DOES have speakers/audio capability. I don't know if this plays into the success of the Streambar connection to this particular monitor, but it works!
NOTE: during Roku set up, when you get to the screen that says the message that you don't have HDMI ARC on this 'TV', simply scroll to the bottom, PAST 'retry', and select the 'my TV doesnt support HDMI ARC' (or something similar to this). I completely missed this!!
The only need for ARC would be if it were a "normal" TV and you wanted the OTA sound to be fed back to the Streambar. Since you're using a display without a tuner, that's a moot point. And since it's not a smart TV, there's no internal streaming apps that would need their audio sent back. So yes, ARC is not necessary for your setup.
Dan Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.