Think you can take a chance here and download a copy of moodle 3.6 - which is now 3.6.3+ - your version 3.6.1.
Unzip it locally. Find the mod directory in the un-archived code on a local machine.
Should look like:
[root@server mod]# ls
assign choice forum label quiz survey workshop
assignment data glossary lesson README.txt upgrade.txt
book feedback imscp lti resource url
chat folder index.html page scorm wiki
Note there are 2 ... the 'assignment' directory is the old version. The 'assign' directory is the newer.
Upload both 'assignment' and 'assign' or the one you are missing. Check ownerships/permissions to match other directories/files in mod.
Let's hope that moodle recognizes there is something to install as one doesn't normally re-installs core components this way.
This is somewhat guessing it will work as there is version file in everything now. So the version file in the one you will upload is actually newer than all the rest of the mods on your system.
You might want to purge caches.
Lesson one should take away from this 'experience' ... don't delete core mods ... if you don't want to use them, hide them instead of deleting. BTW, could be the initial installation of moodle really had issues.
If that doesn't work, one will have to do a minor update to make sure **all** the versions of code are the same.
Best of luck!
'spirit of sharing', Ken