Most new studio chiefs use the announcement of their first-go pictures to send a signal that they want to be taken seriously and therefore associate themselves with big-budget star vehicles. Not recently installed Paramount chairman Brandon Tartikoff, who is clearly proud of his heritage as NBC Entertainment Group chairman. His first movie, the ultracheap ($10 million to $12 million) All I Want for Christmas, has observers wondering if Tartikoff ) knows the difference between movies for TV and movies for the bigger screen. Christmas, a romantic comedy that one agent describes as a ''sitcom episode of Cheers,'' began a rushed 30-day TV-style shooting schedule July 24 to meet a planned Nov. 8 release. But Paramount production president David Kirkpatrick defends his boss' pell-mell timing. ''Casablanca was shot in 28 days,'' says Kirkpatrick. ''American Graffiti was shot in 30 days. All of us in the business looked at the escalating prices and felt there's got to be a stopgap somewhere.'' We'll see where the buck stops on Nov. 8.