These two species are actually quite closely related, so it would make sense that the males would fight each other. Of course, the body language is a bit different, and the rooster has the ability to make displays the cock pheasant cannot.
There are actual hybrids between ring-necked pheasants and domestic fowl, so maybe this rooster had something to worry about.
I don’t think these hybrids occur unless chickens and pheasants are raised together, so I wouldn’t worry about wild pheasants breeding with your hens.
