Okay, I'll assume that by Chinese film star you include mainland China, Hong Kong, and Taiwan (because really, mainland China doesn't even have much martial arts stars).
Chow Yun-Fat: yes he was in Crouching Tiger, Hidden Dragon but he already made his fame with his 'heroic bloodshed' (action gangster films) films with John Woo and Ringo Lam. He also had a few early romance pictures that he was known for.
Tony Leung: again, he was just in The Grandmaster recently but he was made famous for his work with art film directors Hou Hsiao-hsien and especially Wong Kar-Wai (In The Mood For Love being his most notable work). He has also been in films in a variety of genres but never martial arts until 2013 because he was never trained as a martial artist (that may not be true if Red Cliff has him doing significant martial arts scenes, but either way that was in 2008/2009). He was also in two John Woo films.
Leslie Cheung: an extremely talented singer and actor that is known as the 'eternal youth' of Hong Kong. He starred in several popular films and art films as well. One of his first notable roles is in Nomad, a teen film that blurs the line between its genre to become an art film. His most famous work is in Chen Kaige's Farewell, My Concubine, John Woo's A Better Tomorrow, and a variety of Wong Kar-Wai films.
Gong Li: Li is primarily known for her roles in Zhang Yimou's early drama masterpieces such as Raise The Red Lantern, Red Sorghum, and To Live. As usual she did end up making a martial arts film much much later in her career with Curse Of The Golden Flower
Kenny Bee: the star of many cheesy romantic comedies, he's not a great actor or singer in my opinion but he did some great work in Shanghai Blues, basically a tribute to the classic Shanghai films of the 30's.
Anthony Wong: he's not much of a leading man but if you watch a lot of Hong Kong films (especially Infernal Affairs), you'll know him. He has been in some martial arts films but I think he's much more famous for Hard Boiled, The Mission, and the Infernal Affairs trilogy.
Grace Chang: she's Hong Kong's Mambo Girl and of course she was primarily in musicals. She's a lot of fun to watch and she definitely was never in a martial arts film.
Zhou Xuan: one of China's most famous classic singers and actresses, she was around in the 30's before martial arts films were made.
Linyu Ruan: probably China's biggest early silent film star, again there was no martial arts films back then.
Anita Mui: a famous singer/actress known primarily for her romantic roles. I may be stretching though since she's done a few martial arts films as well, but those aren't what got her famous initially.
Kang-sheng Lee: maybe not a "star" but he's well-known among Tsai Ming-liang's fans as he is in every one of Tsai's films. And he is in them almost exclusively which of course means no martial arts films.
Sihung Lung: also maybe not a "star" but he's well-known among Ang Lee's followers for his Father Knows Best trilogy, Lee's first three films.
I'd also like to mention Sylvia Chang but she's actually in several martial arts films even though she is more well-known for her dramatic roles.
I think that the reason why so many martial arts actors/actress are China's biggest stars is because in reality mainland China has very few stars, and the Taiwanese art films are more known for their directors so that just leaves us with Hong Kong cinema to provide stars. And Hong Kong cinema's essentially foundation after the 1950's is definitely the martial arts films. That is really their contribution to cinema because I would argue that nearly all of their popular cinema (which means I exclude Wong Kar-Wai and Stanley Kwan), including gangster films, romantic comedies, horror films, dramas, etc. are built on the foundation that martial arts cinema started with its style of cinematography, staging, even acting. The Hong Kong cinema is very kinetic because of that, and so its stars are able to move out from martial arts or into martial arts with ease.
There is also of course the fact that Hong Kong stars tend to dabble in several genres. Maggie Cheung for example has been in art films by Wong Kar-Wai and Stanley Kwan, martial arts films by Jackie Chan and others, and a variety of comedy, drama, and romance roles. I really don't see much of an equivalent in American cinema where we usually stars of a certain genre. So even many of the ones that I mentioned which don't specialize in the martial arts genres and aren't well-known for it, have dabbled in the martial arts genre especially in recent years (probably due to the neo-wuxia explosion of the early 2000's).
LOL I wrote so much, I just love Chinese cinema!