Within the confines of cognitive psychology, what is the difference between these two tasks? In the literature, playing chess is generally seen as the exemplar of problem solving. But recently (thanks to this site), I've stumbled upon quite a few articles expounding the merit of using video game playing to study complex skill acquisition. This difference in terminology (i.e. chess is a problem to be solved whilst playing a video game like pacman is a skill to be acquired) has me completely confused as to when completing a task is considered a skill acquired/mastered vs. a problem solved.
To take your concrete examples, there are several broad distinctions relevant to comparing a task like chess and a task like playing Pac Man.
Cognitive versus psychomotor skill
Learning versus performance
Task complexity and time frames of learning
This might be a very unscientific answer, but isn't problem solving a type of skill. More specifically, that different kinds of problem solving, are different kinds of skills. I mean that in order to solve chess problems one will utilize the chess-problem-solving-skill?