Could this be made with regular greek yogurt instead of labneh?

You can use Greek yogurt to make the labneh. As I understand it, you add lemon juice and salt to Greek yogurt and then let the mixture strain. Read the article and click on that link about Rivka's comments on labneh. It's a link to her recipe, Homemade Labneh. I wouldn't advise a straight substitution because the flavor and consistent of the tart will be different.