I'm locked out of my 6 year old Chipotle account because they now say my email address is invalid when I login. Here is me asking for their help:
I also reached out to them on Twitter but they directed me to this form. I followed up with them on Twitter with what happened in this screenshot but they are now ignoring me.
No, dots are NOT necessary. Actually you do not even need to supply a domain or a top level domain because mails then default to the default system which is usually localhost.
But even for routed mail there doesn't need to be a dot.
There is still valid Bang-Adressing for UUCP routed emails:
!bigsite!foovax!barbox!me
This is a valid email which basically means "send my email to bigsite, from there to foovax, then to barbox, to the user me."
And if you are in a playful mood - mix FQDN and BANG addressing...
A couple of years ago I made Hotmail crash by sending a mail to googlemail.de!hotmail.com!googlemail.com!hotmail.de!googlemail.ca!hotmail.ca!googlemail.fr!hotmail.fr!... [repeated it for 32kByte] ...!myuseraccount - their server literally crashed completely all over the world for like 15 minutes. I am so proud of myself but then it was their fault for not complying to RfC822.
In fact both are optional. With FQDN-Adressing a user without domain defaults to localhost, with Bang-Adressing there is no @ because the last system is left for interpretation of the last receiver and if he consideres it a user, so be it.