Same happens for me, expect the last line reads
The 'ee==3.6.1' distribution was not found and is required by the application What i did was upgrading 14.04 to 16.04 LTS using the do-release-upgrade. during the upgrade the apt.sources entries for ee where commented out (they point to 14.04 sources anyways).
Before i went to 16.04 i did an ee update to 3.6.1 - everything went fine - and those are actually the last entries in the install.log file. When i try to do a
wget -qO ee rt.cx/ee && sudo bash ee
i get this:
Executing apt-get update, please wait... [ Tue May 24 09:32:03 UTC 2016 ] You already have EasyEngine 3.6.1, exit status = 1
i can not run ee or launch any commands to it.
also the sources are still commented out.
Would love to see a solution, until that - i roll back my snapshot 
Thanks!