I doubt the PCI specifications provide definitions of common English language words like length, breadth, width, depth or height.
Height would be the vertical dimension. Obviously which dimension of the board this refers to depends on the board's orientation with respect to the nearest or dominant source of gravity! For what it is worth I personally would say that 106.68 is the height of the (front edge of) the card. This is largely because the earliest computers with add-in cards that I encountered were Apple IIe computers where the motherboard was horizontal and the daughter-boards were oriented vertically. If the earliest computers had motherboards oriented vertically as in popular tower-cases, I might have been conditioned to refer to that dimension of the plug-in cards as their width.
The dimension perpendicular to the plane of your drawing I would describe as width. But under other circumstances I might well use another word. In a notebook PC we might refer to it as height (for the equivalent plug-in card type).
I would not be at all surprised if different manufacturers used different triplets of terms, nor would I be surprised if their choice of terms was capricious and varied arbitrarily between marketing or technical documents and across time.