I have heard this referred to only as a cousin chart, or "table of consanguinity." As such, it really does not extend a more customary family tree out in additional peripheral areas. Instead, it is another kind of chart altogether, and it really does not resemble the shape of a tree, as does the more customary family chart.

Combining the two types of chart, or extending a tree to include cousins of all sorts, would probably be counterproductive, as the relationships would quickly become too complex to easily and accurately be reflected.

Cousin charts do help a great deal in identifying distant cousins, and especially in figuring out what the relationship terminology means ("third cousin, twice removed," etc.). It is probably best to keep these relationships "treed" separately from your direct-descent ancestors.

Although your answer was interesting, foty, DannoMan has answered my question most comprehensively....
Thank you DannoMan