It is a strange statement, because his description of "level fours" as representing an "ideal round" seems like it would inevitably lead toward the concept of "par." And maybe it did.
My understanding is that the concept of "fours" was no more than a counting mechanism, to simplify keeping track of score. For example, a golfer could say could say "I am 3 over fours" after eleven, instead of saying "I have 47 after 11."
Here is an except from June 16, 1899 Golf Illustrated, discussing the improvement in play and the drop in scoring. Note that golfers had transitioned from counting by fives to counting by fours . . .
But in spite of all this I cannot help thinking that there has been a considerable heightening in the standard of actual play.
A significant proof of this is the way in which everybody reckons the score now by ''fours," and not, as used to be done, by "fives." Players prefer now to say that they are two over "fours" for nine holes, to the old-fashioned "seven under," and this has only happened because the four standard is much more commonly reached or approached than formerly.
So at one time, apparently, golfers used to count by fives. Sometime before 1900 they started counting by fours because they got better. I think that is all "level fours" meant.