Thanks for your message and excuse me for the troubles.
However, I can confirm that it is not really related to Server 2016 (and may not really related to Hard Disk Sentinel at all).
Generally (assuming that the e-mail configuraion is correct, so server, username, password etc. are correct, no firewall blocks the software) there may be two reasons for e-mail problems:
1) Google may block sending e-mails from any application.
Please check
viewtopic.php?f=6&t=10104&p=13494&hilit=gmail#p13494
which shows proper gmail configuration and information about it, what change may be required with gmail account.
2) Hard Disk Sentinel automatically uses the name of the actual computer when attempting to log in to the mail server and begin the authenticate procedure. The computer name may contain some characters (for example underscore or special character) which may not be accepted by the mail server.
Please check the computer name and try to modify at least for a test, just to check if there is any difference.
Newer versions like
http://www.hdsentinel.com/beta4/hdsenti ... -sdsew.zip checks this and uses different method (if required) in order to begin communication with the mail server. Also it has option to always use TLS authentication at e-mail configuration page (which was previously automatically used on port 587). You may try this version - as it may work differently.