The answer to this question can be very complicated only because each country has its own rules and regulations. Exercise physiology is a profession that is recognized in the majority of the countries (especially in the American continent and Europe). The only limitation/issue here is which degrees and certifications are accepted and recognized by each country (not all university schools or certifications are recognized by every country out there). Once you decide where you want to work at then you should contact their education departments and see if your degree and/or certification is accepted by them. In some cases you might have to take a local test/exam that is required by the local regulations in order to be able to work in that field at that particular country. I hope this helps.
Are you asking which countries license exercise physiologists and/or exercise professionals? It has been my experience that all developed nations recognize exercise physiologists as legitimate. You would need to research which countries license or regulate the exercise professionals working there.