In general, commercial Asian beer is very like beer from other continents. Industrial Asian brewers mostly started in the 19th century, based on German lager brewing, and still mostly brew German-style lager. There's also a new wave of smaller breweries that copied US-style craft breweries.
You'd be hard put to it to find anything distinctively Asian about these, but there are some Asian variants developed from them.
In Japan they have happoshu, a kind of cheap beer that uses less malt and more sugar from other sources, simply for tax reasons. Vietnam also has a local variant of quickly-brewed lager beers sold cheaply in the street, called bia hoi.
However, traditional Asian beer as brewed by the farmers for their own use is a completely different story. These exist in places like Bhutan, Nepal, and probably quite a few more places, and are brewed according to local traditions that are totally different from western beer.
Western beer is made from malt, but these beers are usually brewed from raw grain using a fungus that breaks down the starch and makes sugar. Japanese sake (rice "beer") and Chinese huangjiu (rice "beer" and grain beer) are also made this way and could be considered Asian types of beer. Certainly huangjiu made from barley has a lot in common with what we call beer.