He is wearing traditional vestituture, at least up to the point you stated. Old vestituture started with a cassock, over which one put first and amice (a sort of shawl) and an alb which usually had the lace at the bottom you describe. I imgaine this priest is not so eccentric as to use a maniple (a band of cloth hung over the arm), but after putting on a stole, he would then don the chasuble, and often it was a fiddleback chasuble which looks more like a two-sided apron than anything else.
In the movement that calls itself traditional Catholic, these kinds of vestments are still in favor, though to my mind if someone is celebrating a rare solemn Mass it makes the priest look less well vested than the deacon and subdeacon. I had a curate at the parish where I grew up, which had one of the early (and fairly successful) modern style churches forced on it when the old one was condemned, who could not stand that they had not bothered to buy newer vestments, and spent his own money on a very lovely set for himself. To my taste, the modern style of linen (well, let’s face it often polyester) alb covered by stole and a chasuble that fits as an outer garment is far superior, and I don’t think the last couple of popes, who are/were always gorgeously vested, would disagree with me.