I thought that too. Understanding (roughly) its etymology helped me:
skådespelare -> skådespel + are -> skåda + spel + are
skåda = to watch, behold spel = a play, a game skåda + spel = a theatre play are = suffix that denotes a person who performs the action of the verb
Hope that helps you too :)
Mainly since I'm Latvian and can also speak some Russian and both words are nearly the same in Latvian, English and Russian and now I see these two long and difficult words. It's like достопримечательности and other long and/or difficult Russian words, since it has quite a lot of them. Now I know what it means and how to say it, but seeing something like it at first kind of worries you.