While I found a workaround after digging around more, this does not explain why OSTicket is failing to use the built in email configuration. With the configuration as shown above, you get some, but not ALL emails the system tries to send.I found a workaround here: https://stackoverflow.com/a/21891895
Use Fake sendmail for Windows to send mail.
Create a folder named sendmail in C:\wamp\.Extract these 4 files in sendmail folder: sendmail.exe, libeay32.dll, ssleay32.dll and sendmail.ini.Then configure C:\wamp\sendmail\sendmail.ini:
smtp_server=smtp.gmail.com
smtp_port=465
auth_username=user@gmail.com
auth_password=your_password
The above will work against a Gmail account. And then configure php.ini:
sendmail_path = "C:\wamp\sendmail\sendmail.exe -t"
Now, restart Apache, and that is basically all you need to do.