Not only do dots not matter, you can suffix "+ " to your user name before the "@gmail.com" and it will still come to your email address. I actually love this "+" feature and use it a lot .. like send an email to "+bookmark@gmail.com" to bookmark a link, or register with "+nospam" and setup a filter for that address if anyone sends me email on that. This is supported by icloud and fastmail too.
"This is supported by icloud and fastmail too." No, this is neither supported nor not supported by any email provider - it is part of the email specification. It works that way with all email systems, unless they are non-RFC compliant.
It is not a part of RFC5322, RFC2822 or RFC822 - nothing in those RFCs establish any particular semantics of local-part (the part before "@"), and in terms of syntax IIRC those RFCs only defines the escaping rules (backslashes, quotes, etc).
RFC5233 mentions the established practice of using a separator character that splits local-part into "user" and "detail" pieces, but does not standardize any particular syntax for the separator (it cites "+" and "#" as possible examples). Moreover, this RFC is about Sieve language, and it is out of its scope to define such standard for email addresses.
RFC3696 mentions "user+mailbox@example.com" but does not define any semantics, merely citing this as an example of a valid email address, then going to how it must be escaped in a mailto: URL.
It is completely up to a particular provider to implement (or not) any subaddressing syntax and any logic related to it. No email specification I'm aware of makes this a requirement. (It's not like I've read every email RFC thoroughly, though, so I could be missing something.)