I think there's a subtle difference in meaning. "Having around on the pitch" says that they are useful to the team's game as whole. "Having around them" implies a rather more intimate connection - the players like to have him close to them on the pitch.
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AnonymousHe’s a player others appreciate having around them on the pitch.Here, he is around them, not they around him; in other words, they (others) appreciate he is with them on the pitch.