Not really “trans”!
Klinger claimed to be a woman, and dressed like a woman. He didn't have hormones or surgery, but in fact most of the "trans" people today do not have surgery, and many do not take hormones.
All it requires, to be considered "trans", is to claim to be of the opposite gender.
Which is exactly what Klinger did. Granted, we all knew he was faking, but so are a lot of so-called "trans" people today, e.g. these guys in prison who get transferred to the women's prison, without surgery, and start having sex with the real women.