Comparing & contrasting decision problems and normal games

Decision under uncertainty is sometimes called a "game against chance", and can thus be modeled as a two-player normal form game: the decision-maker vs Nature/Chance. The possible states would form a set of pure strategies for Nature, and Nature commits to a publicly known mixed strategy that randomizes over those pure strategies (assume Nature is indifferent between all outcomes so that the mixed strategy is rational). The decision-maker's best response to this known mixed strategy is equivalent to the choice that maximizes his expected utility in the decision problem. In this sense, decision problems are really just a special case of a game.

The above suggests that your statement

A decision problem deals with expected utility, whereas normal form games do not.

is incorrect, since normal form games do deal with expected utility, especially when proper mixed strategies are involved.