1630s (athletical is from 1590s), "pertaining to an athlete or to contests of physical strength," from Latin athleticus, from Greek athletikos, from athletes "contestant in the games" (see athlete). Meaning "strong of body; vigorous; lusty; robust" [Johnson, who spells it athletick] is from 1650s.
word-forming element making nouns implying a practice, system, doctrine, etc., from French -isme or directly from Latin -isma, -ismus (source also of Italian, Spanish -ismo, Dutch, German -ismus), from Greek -ismos, noun ending signifying the practice or teaching of a thing, from the stem of verbs in -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached. For distinction of use, see -ity. The related Greek suffix -isma(t)- affects some forms.
<a href="https://www.etymonline.com/word/athleticism">Etymology of athleticism by etymonline</a>
Harper, D. (n.d.). Etymology of athleticism. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/athleticism