In English there exists an interjection -- "For shame!" -- which expresses disapproval.
Johnny, did you really take cookies from another child's lunch box? For shame, for shame!
The parenthesized comment explains that the previous "for shame" is not that phrase but simply a way of wording "because of shame". But then, the author could have just written "because of shame" and omitted the explanation. So it is clear that the author wrote "for shame" followed by an explanation deliberately, in order to play on "For shame!", in order to sneak in an expression of his or her own disapproval of the situation.
"Which is a shame" is simply an expression that the preceding situation is unnecessary, wasteful or regrettable in some way.
Note that in "for shame", as used by the author, the "for" means "because of" (we have to take the author's word for it). But in the "For shame!" interjection it doesn't have a meaning. The expression is an idiom without any literal interpretation according to any general rule of grammar. We can hypothesize that "for" plays the role of a special particle for starting such interjections, and it may simply have been copied from expressions such as "For God's sake!" in which it does play a normal grammatical role (literally saying "for the sake of God"). Another expression with such a "for" is "For crying out loud!".