Formula 1 is a form of motor sport with its own rules and regulations, just as World Rally Championship has its own rules and regulations, the same as K-1 which is a form of Kickboxing has its own rules and regulations and Muay Thai which also has its own rules and regulations and so on for Full contact etc, they all have there own rules and regulations.

You are quite right the fighter would like to be refered to as K-1 Champion, Glory Champion, and Muay thai Champion etc, but they are also Kickboxing Champions! The same way Lewis Hamilton was 2008 FIA Formula one World Champion he was also a Motorsports World Champion telling people he is an F1 Champion allows people to know what type of motor sport he is a champion of! the same way telling people you are a K-1 Champion tells people what type of Kickboxing you are a champion of!

if you said to someone im a K-1 Champion and they said whats K-1 and you said " a stand up fighting promotion allowing combatants to use punches, kicks and knees" you would sound silly and the person you were talking to would probably give you a strange look.