Let me second what has been said and add a few comments.
First of all, at its most basic level, "DOE" simply means a designed experiment. (As opposed to what - a random experiment???) Any experiment that has been planned to accomplish a specific purpose is a DOE
Traditionally, "DOE" has become synonymous with the use of a particular set of standard designs - 2 level factorials, central composite, Box-Behnken, Taguchi, ... These designs were created by experts so that they can efficiently accomplish specific purposes. When used properly, these designs are quite effective.
At some level, the standard designs are just sets of hypothesis tests performed simultaneously. For example, a 1 factor, 2 level factorial experiment tests 1 hypothesis: does changing Factor A make a difference? A 2 factor, 2 level full factorial tests 3 hypotheses: does changing Factor A make a difference, does changing Factor B make a difference, does changing both factors at the same time make a difference? As you add more factors and more levels, you have more hypothesis tests. When you do a frctional factorial, you remove some of the hypothesis tests.
I suppose you coud say that choosing the proper design allows testing of all the hypotheses you are interested in without too much extra work.
Tim F