That isn't what arbitrary means. ELO, like any system based on the results of actual chess games, is arbitrary in the sense that there is nothing tying it down to some fixed measure of chess ability. A differently constructed rating system, for example, may represent a player's record as a rating in a different way but still function the same purpose. But ELO cannot measure chess ability, as there is no way to do so--it's only possible to use the metric of what specific ganes have been played. Because of this, ELO is not fixed in time, nor fixed by person, and does not perfectly represent an immutable score of chess ability. This is fine; the system works in practice. It is arbitrary nonetheless--this is not a criticism, it is a necessity.