How many times have you seen a crew 'too overloaded' to select reverse! Dozens of times by me. If thrust levers were in any position other than closed, spoilers won't deploy and reverse locked out. The most likely scenario is thrust is UP either because of TOGA selection or a manual selection. Thereafter it is a bun fight as to who is flying. Interestingly there doesn't seem to be much rudder deflection during the video. Nosewheel steering would have been hyper sensitive at that speed which may explain the severe skidding.
To me, it looks like the plane may have been accelerating after nosewheel touchdown. It certainly wasn't decelerating.