Can a summary judgment order also be a dismissal order?

This one's for YOU appellate nerds!
Yes, we know that an order granting summary judgment is not an appealable order. But what if that order also includes a dismissal? We also all know that under CCP 581d, a dismissal order IS a judgment. So what's the ruling? Appealable or not?
Your answer is finally here, in this unpub from 1/1: Tianen-Bennett v. Superior Court.

(Note, that we're NOT talking about CCP 581 "subdivision (d)," but "581d," a different statute with a weird name. If the opinion gets published -- and won't some appellate-minded fanatic demand that? -- then the decision better be proofed carefully!)