I would start by checking your network drivers in the network and sharing center to see if the hamachi network adapter was installed correctly. ( also your screenshot link you posted is broken).
We were having the same "failed to connect to engine" issue on mac os el cap / sierra.
Our solution was:
hopefully this helps others as well.
On 50% of the Updated Windows 10 Creators Updates the Hamachi Adapter is Damaged and resulting in Yellow Triangles, only a Deinstall and Reinstall is working.
I had same (or just similar) problem and solved it by renaming the Hamachi Network Adapter to "Hamachi" from "Ethernet 3" (which it was named inadvertently, somehow, not by me)
I got this problem also after I switch back from Windows 10 to Windows 7 for compability hardware problem. After go in Win 7 and download latest Hamachi from website I can't solve this triangle problem by every explanation I get from internet. Fortunately, I remember I still have my hard drive backup in 2014 and find my old Hamachi saved ver 184.108.40.206, driver date 14/05/2007. After I installed it the triangle problem dissapear and my Hamchi can connect to the network. I didn't do update and just use my old Hamachi. Hope this will help you.
There was yellow triangle left of connected pc and when I clicked it said tunnel error. Then I run diagnostic and there is tunnels yellow and in info it said problems found. I clicked on details and there it said "Peer details:
DESKTOP-PKT5F1H VPN domain's tap device is down". I know there is similar topics but I read them all and i didn't find solution. I tried in services md reset hamachi connection, then I renamed adapter in "Hamachi", also I tried reset hamachi2 in task manager. Nothing of this solutions in all that topics about this subject didn't work so I open new fresh one and hope someone have good solution. Or if there is no good solution what is good alternitive for this hamachi so I can download it and play with friends without stupid peer and tunnel errors?
я не могу запустить Hamachi пишет
Hamachi self-diagnostic result file
Date2017 - 12/22 16:45:29.044
File not found: hamachi.cat
File not found: hamachi.sys
File not found: hamdrv.cat
File not found: hamdrv.sys
after installing security patch 2018-001 in macOS high sierra 10.13.4 Hamachi won't connect...."fails to connect to the engine".
I've tried uninstalling and installing again with no positive results.
Other issues noted before such as allowing the developer in the mac settings, don't work either, I believe this is a totally new issue caused by the mac update and there is no way to revert it.