Hi Chris,
Thanks for reporting this issue.
I am able to replicate this issue locally where the left sidebar toggle is indeed not showing for non-logged in users in mobile mode.
I have logged this issue in our tracker and the devs have fixed it. The fix will be included in the next release of EasySocial.
In the meantime, if you like to have the fix now, you can download the attached fix file below and apply it into the following directory:
JoomlaFolder\components\com_easysocial\themes\wireframe\dashboard\guests\default.php
Let us know how it goes if you decide to test this fix.