In this case, it's conditional. Even assuming the tree is dead it could be a reasonable anchor, but it depends on a couple of factors. First, what loads is the anchor going to see? On TR, you usually don't have the risk of a high-force fall, but if the route has significant overhang or traverses, you need to be more careful. Second is how strong is the tree/root? In this case, I probably would attach myself to a better anchor uphill and then yank on the trunk and roots to test how solid they are. Tree type also matters - from the little bits of bark & green, I'm guessing this is a cypress of some kind, and they're very rot-resistant. OTOH if it were something like a birch or a pine I'd be a more hesitant to trust the dead wood.

Putting the third leg of the anchor into rock is a good insurance policy on top of that.