Part of "runner's face" comes from running outside a lot without a hat, and without sunscreen. Sun causes wrinkles. Run at sunrise, sunset, or if midday, with a hat, UV-sunglasses and sunscreen. It can be prevented.
Also, running makes you thin. You lose weight. Think of a raisin. It's a shrunken grape with some wrinkles. Blow it up like a balloon and it becomes a grape with smooth skin. That's what happens when you gain fat, in your body and face. It stretches out your skin flattening out the wrinkles. But it's only temporary. Eventually the skin adapts and then you're heavier, with wrinkles.
But mostly "runners face" is a way for out-of-shape haters to put down runners to make their out-of-shape selves feel better.
Even if runner's face is a thing, I personally, would rather be a little gaunt with a few extra wrinkles if I feel better and fitter. But that's just me.