If I recall correctly their documentation suggests that a single login to the Gmail web app or several other properties should count as well as the official Gmail apps, but no web logins I tested had any effect for me. Sadly I can't retest this without setting a new timer on an account.

If you end up in a position to tet this you'll want to keep an eye on multiple account logins as well since the link they send you in the warning doesn't go to a specific account. If you're logged in to more than one account and the first one isn't the one you got the warning about you'll end up looking at the manager for the wrong one and need to either log out entirely or find it manually. A minor design issue, but it can be confusing for a few minutes.