Which meaning of "take" in a dictionary is used?
"Yet another arena where multimedia is becoming important is in computer games. Games often run video clips to depict some kind of action. The clips are usually short, but there are many of them and the correct one is selected dynamically, depending on some action the user has taken."
"take (an) action" is a set combination of words. g. com/en/definition/take : Make, undertake, or perform (an action or task)
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"take (an) action" is a set combination of words. You can find the relevant sense of "take" e.g. at sense 6 at https://www.lexico.com/en/definition/take :
Make, undertake, or perform (an action or task)