Prima vista one could indeed be inclined to think that the German word Art is derived from Latin ars, artis, which would justify the translation you quote.
However, a quick look-up in Grimm's Deutsches Wörterbuch 1 for Art seems to dismiss that idea: there Art is reported to be of somewhat unclear origin; not to be met in Althochdeutsch, more frequently in Mittelhochdeusch, and possibly related to Slavonic rod (kind). 2
Anyway it is predominantly used in the sense of "kind, manner", not "arts".
If this is correct, the translation you quote is misleading, and a better one would be:
Essay on the right way of playing [keyboard instruments?]
Most crucial for knowing what C. P. E. Bach actually meant would be to have a look on the use of the word in Bach's time. Perhaps somebody else can contribute this? (Google Ngram is no help here - if considered reliable at all - because the corpus used for this database starts with books from 1800.)
Grimm's Deutsches Wörterbuch lists in total 6 meanings of Art, most refering to something like "kind", "manner". Number 6 however goes more into a direction of "artfulness, dexterity" (Manier, Geschick, Tüchtigkeit) which then would be something like a mix of "Art und Weise" and "Kunst". This then could be used as an argument to support the translation you quote:
Essay on the true art of playing keyboard instruments
However, I personally feel uneasy with that. For me - as a German - the English "art" is too much into the direction of "Kunst", whereas in "die wahre Art, das Clavier zu spielen" at least both ideas seem to be included: "Kunst" and "Art und Weise".
But perhaps we are making things more complicated than they actually are. Perhaps Carl Philipp E. Bach had nothing other in mind than Art in the usual modern meaning of "manner" or "way" and would laugh about our attempts to assign a Kunst-meaning into his book title just because of an obscure English translation.
(Another thing to consider is how the English art was used in the English speaking world at the time of C. P. E. Bach, i.e. mid 18th century. If art was used in the mixed sense of "manner plus dexterity", the use of art in the book title would be justified, at least as long you are seeking for a contemporary translation. For a modern translation I find it still misleading.)
1) Source for "Art": http://woerterbuchnetz.de/cgi-bin/WBNetz/wbgui_py?sigle=DWB&mode=Vernetzung&lemid=GA05720#XGA05720
2) I would suppose (but I haven't looked it up) that there will be a common Protoindoeuropean root like * rd that sits behind all those words - German "Art", English "art", Latin "ars, artis", Slavonic "rod" because the meanings always intersect. From "what kind of" to "how to" to "the good way" or "the high quality way" it is only a tiny shift of meaning.