Spurred hens happen because the birds have a really high amount of testosterone. OEGBs are only game in name. But game chickens that are still fought today commonly have spurred hens. Many breeders don't like this as it makes it easy to break the eggs in the nest. I find that personally I like spurred hens, and have found I have one particular cock that throws spurred hens quite often. But he is a Phoenix.
It is caused by high testosterone levels. Alot of those hens won't lay very many eggs before they set. I have one spurred hen that lays 16 eggs a year, in two separate clutches, 8 each. But she throws AWESOME stags.
There is a fine line between to many "male" characteristics in a hen and just the right amount. The more the hen looks like a male, the more masculine her stags will be. So the hens that have long tails, red in the neck and saddle, spurs, and an occasional crow, tend to throw great roosters.... that is, if you can get any eggs from them....
But to answer your question, No. All game hens do not have spurs. You can breed for it or against it, depending on where your priorities are.
Alot of Longtail hens also have spurs.