Pretty much yeah.
Those two towers are the main supports for the new roof. They each contain 5 escape staircases, a passenger lift and a goods lift, plus a couple small ancillary rooms that vary on different levels (telecoms, prayer, first aid room, pantry etc). At the top level the big part of them is VIP rooms and suites, with only one stair all the way down at that point, the other 4 replaced by larger rooms out to the stadium. My guess would be the lift is a dedicated sky-bar lift to go straight up to the vip bits, and not one that will stop at each concourse. But overall, they are the main structural 'cores' that take up the new roof and link the new concourses and seating tier to the office and hotel at the back.