Firstly, the Tampermonkey sync setup is described here.
The above-described process is not working for me, however. I've written a few scripts on one machine, where Chrome Sync is enabled, and have enabled the same sync functionality on a couple of other machines, neither of which are picking up the scripts. On all of the machines, Chrome is logged into my Google account.
I wondered if there might be some kind of delay, but everything has been setup for nearly 24 hrs at this point, so I don't believe that is an issue.