There several ways to determine if a font is available through Monotype Library Subscription.

First - in the search terms you can set a filter to display fonts only available through the subscription.

Either in the top search bar

or or the search page itself

Second - under search terms or family pages you can see a "M" logo next to it's available use listed.

In search you can select "Preview" on a roll over which displays the ability to install or assign a font to a web project.

On a family page, the ability to assign a web font or install the whole family or individual style will be on the right hand side