Thank you for your question.
First, Muay Thai is a martial arts that originated from Thailand.
However, K-1 is a martial arts organisation and brand, which is the organizer of K-1 fighting events worldwide.
But still, K stands for the letter K which is officially designated as a representation of words from Karate, Kickboxing, and Kung fu. So K-1 is mixed martial arts games (or match).
In that sense, kickboxing is both a sport and martial arts too.
I hope this helps you to satisfy your curiosity.
Thank you.

PS: This is not the opinion of ICM, but the personal thought of the respondent.