No GAPPS are not required at all. Just got it working on a CLEAN no-GAPPS Cm13 on One Plus 2 after a long search and tries.
How to Get TEAMVIEWER QUICK SUPPORT properly working (even may work on those phones which are not supported)
1) Install Quick support from playstore or any reliable apk store.
2) after installation , if supported it will ask you for downloading/installing QS addon .
In my case it even didn't ask for that, so installed teamviewer host. . install it. after opening, it will download QS addon to download folder of your card. If you still dont get QS addon, try downloading it from stores like apkpure or aptoide etc or take from someone else
In case of Teamviewer host way , you will get an error after download as "NO MATCHING ACTIVITY FOUND" and if you are installing from other sources, it will not install at all
3) Copy the QS addon.apk to /system/priv-app folder (CM13 didnt allow me to paste in /system folder even with proper mounting and root)
4) Fix permissions of QS addon apk to 644 (all ticks on Read and only 1st tick on Write) like others in that folder
5) Restart mobile and QS should work full. Without addon, only file transfer & stats will work.
File versions : Team QS: 11.0.5112 & QS addon : 10.0.3086
I am writing this bcoz i felt so bad being not able to find any solution for > 6 months. Hopefully it helps you
P.S. One plus 2 Users i am sure u were never able to get teamviewer working on even OOS 2.0 & OOS 3.0 ROMS.. Try above method and it should work