When Chinese people go out for dinner do they call it Chinese?

More often than not, no, they will not directly say they are going out for 'Chinese'. There may be a question of whether they want Asian food (中餐) or Western food (西餐). What they will say is a more specific location or type of food. Some examples include : hot pot/steamboat (火锅/huo guo), noodles (面/mian), food from northeastern China(东北菜/dong bei cai), Shanghainese food (上海菜/shang hai cai), etc.