It isn't a new name on the trophy, that means a club who has never won it.
Plus the Clubs are in charge of the PL, as they own it.
I think it means every 6 years they want someone who hasn't won it in ages winning it. I don't think it's absolutely specific to 'never having won it before'. The thing is, they can't rig it for someone useless to win it - they have to be close first, so it limits the amount of teams it could be.
If it was Blackburn going for it, then they'd be a 'new' winner, but they're obviously way out of things.
It's so long since Arsenal have won it that they are practically a 'new' winner.
Reading between the lines, the PL definitely wants the league to not be a one or two horse race like most others are. Arsenal winning it is different, a lot of fans won't remember the last time they won it.
Now that united are halfway decent again, they could also be a new winner in a couple of years, with some help, obviously.