I assume the amp rating is important for the AC adapter only?

Not quite. It could be important in the sense of "This boom box might draw as much as 2 amps sometimes". In which case, you have to make sure the cigarette lighter wiring in your boat is rated to handle 2 amps and/or doesn't have a fuse that's rated lower than 2 amps. That's not likely to be an issue (the fuse is probably 10a or more), I just wanted to point out where the AC adapter's rating might be important.