It appears Hamachi still technical is running as a service but they have chose to monitor by some other means whether the user is actual active or not. If the computer is on the lock screen where you select the user account to login to (even if a user is actually logged in) Hamachi will turn off.
For the above mentioned reasons I have decided to switch to NeoRouter. NeoRouter so far appears to do everything Hamachi did and then some. Built in Windows Remote desktop, Wake-on-Lan, shared folders, command line interface, run from USB drive, network bridging, etc. The only catch is you need one computer that is always on to act as the "server" to tell the other computers how to connect to each other.
A note on setting up the NeoRouter server: When I first installed it it would not connect (which you can test via https://www.neorouter.com/Dashboard/domainstatus.aspx). I solved this by checking the Windows firewall and noticing the NRServer and NRService exceptions were being blocked in my private network.