I would say they eat a smaller proportion of meat. Many Asian dishes do have meat but it's just one out of many ingredients, including rice/noodles, vegs, spices, etc. While in the West sometimes we just eat meat with a side of potatoes or whatever, maybe some spices but the majority of the dish by mass is meat.

I agree that it's not necessarily easy to find dishes with no meat at all in Asian countries, though.

It's probably a better strategy to try to convince people to eat less meat per dish (as in many Asian preparations) than to go vegetarian, anyway. At least it would be easier to convince me, that's for sure... if my country had the hawker stalls that they have in Singapore, I would already be eating less meat.