Why 青椒牛 instead of 青椒牛肉 in this Chinese menu? See the attached Chinese menu. Why L4 is called 青椒牛 instead of 青椒牛肉? I think 牛 means the animal cow (or ox?) and 牛肉 means beef.

Similarly, why 芥蓝鸡 instead of 芥蓝鸡肉？
I am not sure how it sounds to Cantonese ears or Chinese-speaking population outside China, but in Mandarin spoken in mainland China, 青椒牛 is absolutely weird, and sounds like the cow is cooked in whole (uncut). 

However this usage is extremely common in Chinese restaurants in the US. I heard it's similar in other English speaking countries. No idea why it evolved like that.

Aside from the improper omission of the meat form (肉/丝/片/etc.), the lack of cooking method (炒/烧/烩/etc.) also sounds off. In mainland China even in very casual spoken language, those words are included out of habit. It will actually take effort to omit them.