I don’t have a really good answer, but I will try since you asked.

I think Seymour, when he wrote his book (Antique Gambling Chips), had access to a lot of old turn of the century catalogs, which listed chips for sale to the public. He knew those chips were generic.

Also, private order chips typically have initials or a name on the chip. Generic ones had images of animals, things, or abstract designs. Generic chips were also usually on some version of the plain mold (engraved, die-cut, embossed, etc.). Once you see enough of these chips, you get a general sense of whether they are generic or a private order.

I believe a few of the chips in his book and your guide were probably private order chips, but they are similar to the old generic chips, so they kind of fit in with them.