From my waterline models of Titanic and Queen Mary 2 I'd say that the picture looks about right.
A lot of factors affect space comparisons. A standard cabin in a modern cruise ship would be around the same size as first class cabins in Titanic and not all of them had their own facilities. On Titanic the bulk of the passengers were steerage and accommodated in bunks. Cabin space takes up a lot of space in a modern ship, you only need to look at all those balconies!
As far as the other space in the ship is concerned, much of the hull of Titanic was taken up with boilers and machinery whereas on a cruise ship the power to weight ratio of the diesel power plant is much, much greater and the propulsion is often in the form of pods hung underneath the ship. Use of aluminium makes for a much lighter upper structure on a modern ship, permitting more accommodation decks. Titanic was deep draughted and sat in the water, Allure of the Seas basically sits on it and despite her much greater size actually has a draught of 1m less than Titanic. Most of the rest of the difference is accounted for by public facilities. The Titanic didn't have things like outdoor lidos and swimming pools, theatres, golf courses, water parks etc. etc.
But of course the two ships shown are quite different types. Titanic was an ocean liner, Allure of the Seas is a cruise ship - different animals.
Colin