Is Postfix required for WordPress contact forms in general?

You don’t need Postfix if you use an SMTP plugin like, for example, WP Mail SMTP. Such kind of plugins can send email from your Google account via SMTP.

I have just checked it by stopping postfix and successfully sending an email via WP Mail SMTP.

If no SMTP plugins are activated on your site, you definitely need system transport, which can be Postfix or another mail transfer agent (MTA) on Linux. Postfix also can send your emails using your Google account as a relay.