Lets look at the picture first. Sir Thomas is seated where the entrance to the Billiard room now is. He is facing a door leading into a room. In Shakespeare’s time we would not expect that door or room to exist although by the 1690’s Charlecote has a painting showing a small extension in that position. Maybe the artist knew about that extension and extrapolated it back to Shakespeare’s time. The floor tiles shown in the picture are the Florentine tiles present in the hall today. George ordered them on his trip to Italy and they were laid in the hall in 1844. In Shakespeare’s time the hall had large flagstones which were taken up and reused in the new Victorian kitchen where they can still be seen.
So I think we can conclude that historically this picture is of no importance.