I think it is important to point out that the speaker isn’t saying that these are the only virtues, but rather these are the virtues of prayer. My interpretation of what he means by that if these qualities need to be present in the person doing the prayer in order for the prayer to be effective.

A faithless, irreverent, insincere, disloyal, proud prayer probably will overlooked.

To answer your question, I think there are other virtues that bring peace/comfort. Patience, for example, can bring peace/comfort. Others include kindness, forgiveness, and self-worth.

I think the fact that faith motivates us extend its status as a virtue.

Something is a virtue if it brings peace/comfort.

Faith brings peace/comfort, therefore faith is a virtue.

That seems straight-forward enough. My next question, then, what other things that provides peace and/or comfort also qualify as a virtue? Do you think faith has any other attributes not listed that make it a virtue?

The first and most fundamental virtue in effective prayer is faith. A belief in God brings peace to the soul. An assurance that God is our Father, into whose presence we can go for comfort and guidance, is a never-failing source of comfort.