In America, beer is made with rice when they don't want to spend the money on more expensive grains. For example, Busch beer is a rice beer, but Bud is made with a normal mix of grains. Hence the price difference. Neither is something that I drink on a regular basis anymore, but I supported them heartily in college.
All beer has malt in it and there are very few true rice beers in the USA. Budweiser uses rice as an additive and Busch uses corn. Corn's use in Busch is primarily to make it cheaper and it has minimal effect on the character of the beer. These and similar beers are still based primarily, usually at least 75%, on barley malt but use other grains as a filler (the non-malt fermentable contents are called adjuncts in brewing) so that the relatively more expensive barley content can go down but you still get a sufficient source of starch. It's the starch that is the fermentable sugar the yeast consume.
Using rice, corn or other sources as a filler is generally just a way to make beer cheaper at the commercial level, but they can have specific uses. Oatmeal, millet, potatoes and rye for example are actually quite legitimate adjuncts, like used in an oatmeal stout, for example. Wheat and rice are also very often used in beers for reasons other than just because they are cheaper. Having a high wheat content beer, a Weißbier or wheat beer, gives you a distinct beer. A Weißbier is about 30% to 50% wheat in the grist bill and really aren't any cheaper to make than an all barley beer.
Rice is an odd one because it's usually cheaper than malt and that's often why the big brewers use it. But it also has the ability to lighten up a beer's body and that's partially why it's used in Bud. AB formulated Budweiser to be as non-offensive to as many people as possible and still be economical to make.
Japanese beers often use rice for the same reason, it's availability, and that's why their beers tend to be what's called dry. They have a very crisp bite and taste. Some speciality styles use lots of rice and are closer in truth to sake than beer. If the malt content grows small enough (some are below 25% malt) the Japanese actually have a proper name for it, happoshu. So I dunno if that Heukmi is a total rice nihonshu or if it has malt in it. Not being able to read Japanese, I couldn't figure it out from the label and the Aizu Wakamatsu website wasn't much help, either. I'd heard it was a 100% rice beer (i.e., almost like a low alcohol, carbonated sake), but the more I think about it I'd guess it's just a very low malt content beer. In any case, I've heard it was a pretty brutal beer and so I didn't want to risk $6 on a bomber before looking it up.
BTW, here's the AB fact sheets on their beers:
http://www.anheuser-busch.com/BeerVerified.html