So when you say 'the Asian market' you gotta understand that it's radically different depending on which country you're dealing with. You bring up baseball, so I'm gonna assume you mostly mean east Asia, and specifically Korea and Japan. Baseball has been popular in Japan since the Meiji Era, due mostly to deliberate westernization as part of its attempt to modernize. Baseball likewise has some history in Korea following its annexation by Japan in 1910, but really only exploded in popularity following the Korean War as South Korea essentially became a US protectorate. So there are major historical factors there that pushed interest, and in the case of Japan these were artificial and intentional.
Japan and Korea are realistically the best places to see growth in hockey interest in east Asia.. You have real winter climates, you have existing interest in winter sports, ice skating is popular there, and they are extremely wealthy countries where kids who are interested in sports can actually buy lots of equipment. All critically important factors. The Japanese women's ice hockey team has qualified for the last three Olympiads, which is an interesting development, and probably a really good indicator that the sport has some legs there.
The NHL briefly flirted with China when the NBA thought it was going to be a golden goose, and then wisely cooled off on that idea. There are a lot of cultural, economic, and political reasons why that isn't going to work any time soon. I think if the NHL wants to play exhibition games -- or even an international series -- in an east Asian market, Japan is the obvious choice. Whether or not anyone in the league office has a brain to figure that out remains to be seen.