That chair looks like it has a control panel wrapping around the front of it. You can see the platform has a section of it that curves back into the centre and then back out again right in front of where the chair is.
Also, it appears there is the same sort of setup on the opposite side of the platform. Next to David you can see the outline of the chair.
Lastly, if you look at the chair you can see that there is a slot in the ground that it must slide backwards and forwards in.
When David first enters the room everything is dormant, the only light is that of his flashlight and what comes through the dome. In fornt of him a set of steps is cut into a circular platform with four sealed sarcophagi. He (or something) activates the machinery, a covering between two of the sarcophagi slides apart revealing a control desk and an egg-shaped chair slides from the outer wall. David activates the control panel bringing up the holographic imagery...