Yes and No
Yes, the Premier League started in 1991 and, yes, this is the first time Liverpool have won it. But it was hardly a new league, it was simply the rebranding of the FA Division One which was the top flight of English football for over a century. So nothing has really changed, a winner of the Premier League or the old Division One both have earned the right to call themselves Champions of England. Liverpool did the latter 18 times before now also doing the former and, for me at least, a rose is just as sweet by any other name and both achievements - winning the old Division One or the current Premier League - deserve equal credit.