Such penalties result in a player being sent to an isolated area called the penalty box, after which the offender’s team must operate a player short. IMO, to operate is strange in sports, seems too technical. I'd say.
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Should i regard a player short as adjective ?No. It's actually adverbial here. It acts as an adverb of manner, saying how the team must operate. (It does not answer the question "What kind of ....?", which is what an adjective answers.)