Just want to post in case anyone comes from an internet search...
I, too, was having issues with Reaper hijacking my sound card. Even if I stopped playback on Reaper and switched to Chrome and tried to resume playing a YouTube video, the video would spin.
TL;DR - I had to do 2 things:
1. Disabled all other audio devices on my system (and keep it that way).
2. Ensure that Reaper and Windows were both using the same sample rate.
My Reaper settings were for 24-bit, 88.2k
My Windows 10 settings were for 24-bit, 44.1k
That was causing the problem!
Once I did the above 2 steps everything worked. I did not need to enable Reaper's option "Close audio settings when stopped and application is inactive". Your mileage may vary, but just posting what worked for me!
Windows 10 Home
Reaper 6.79
Mackie Onyx 1620 (the older Onyx, not the i-series) with the Firewire card
Mackie driver for anyone interested.