"Culture" in China means supporting one party feudal style rule, and in this case in particular "culture" means "accept the revolutions, ccp thought, ccp economics, and the ccp's right to all authority."
Anything less would be 'un-' or 'anti-Chinese'.
The culture Jiang mentioned in his speech is so-called 'mainsteam' culture which was defined by Mao in 1942 as the culture that serves the revolutonary politics and the working class. Typical examples are the model Beijing opera during the cultureal revolution. Note that the model opera is still popular among middle-aged people who experienced the revolution.