As joeqwerty rightly points out, it doesn't show
smtp.google.com because a
MX record indicates where mail servers should send messages destined for that domain. This is not the same as the servers that should be used by an end-user's e-mail client to transmit outgoing messages to arbitrary destinations.
RFC 6186 describes a method for automatically detecting a SMTP server with
SRV records. The problem is that for the majority of the internet's life, SMTP server settings have been conveyed through documentation and not through DNS. You can't rely on this information being present. Modern e-mail clients will attempt to automatically detect the SMTP server settings based on the domain suffix you provided, but if that fails the user has to rely on that company's documentation as usual. This information is not otherwise available, electronically or otherwise.
submission: Identifies an MSA using [RFC4409]. Note that this
covers connections both with and without Transport Layer Security
(TLS) [RFC5246] as defined for SMTP in [RFC3207].
Example: service record
_submission._tcp SRV 0 1 587 mail.example.com.
In this particular case, the query you needed was
_submission._tcp.gmail.com with a type of
$ dig _submission._tcp.gmail.com SRV
; <<>> DiG 9.9.5-9+deb8u10-Debian <<>> _submission._tcp.gmail.com SRV
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 8996
;; flags: qr rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 0, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4096
;; QUESTION SECTION:
;_submission._tcp.gmail.com. IN SRV
;; ANSWER SECTION:
_submission._tcp.gmail.com. 86400 IN SRV 5 0 587 smtp.gmail.com.
;; Query time: 9 msec
;; SERVER: 22.214.171.124#53(126.96.36.199)
;; WHEN: Sun Jul 02 03:17:11 UTC 2017
;; MSG SIZE rcvd: 89