Rooted. Used towel root demoed by DroidmodderX here
How To ROOT ATT Verizon Galaxy S5, Note 3 and ANY…: http://youtu.be/i6EVPeHkz4k
The two biggest issues u had were the fact that the tr apk wouldn't download to the phone. I suspect that was a Chrome issue. I downloaded to my Nexus 7,uploaded to drive and put it on my phone from there.
The second was getting the damned back of, after I booted to download to see if it tripped Knox. It didn't ☺
dmx posted that there was an issue Wtf the su binaries on supersu using the play store version, and linked to a beta. I couldn't get the beta to install, fire whatever reason. But the play store version (1.97)worked just fine.