For everyone else with this or a similar problem:
The latest half working version of ZeroTier on (x64) Windows 8.1 (Pro) is 1.8.3.
One still needs to install version 1.6.6 [1] first and make sure it works and so on.
Then upgrade to/with version 1.8.3 - this will keep the VNIC/TAP driver from 1.6.6 but everything else will be from the almost current version.
Note: It may be necessary to re-install 1.8.3 more then once and/or install the VNIC/TAP driver manually[2].
It seems not only windows 7 support was dropped with versions > 1.8
see here
[1] see official download page or:
https://download.zerotier.com/RELEASES/1.6.6/dist/ZeroTier%20One.msi
[2] (I can’t post more than two links in on post…)
https://zerotier.atlassian.net/wiki/spaces/SD/pages/35455014/PORT+ERROR+on+Windows