No. It is much more important that they understand the subtleties and intricacies of game design (which is why folks in the games media are more likely to go into game design than they are to become professional esports players). They should also know how to write about and communicate their experience effectively.
In some cases, though, there are games that are so deeply tied to technical skill (fighting games, competitive shooters, etc) that they should at least be well versed in high-level play. But again, they don't need to be unusually skilled.
In some cases, though, there are games that are so deeply tied to technical skill (fighting games, competitive shooters, etc) that they should at least be well versed in high-level play. But again, they don't need to be unusually skilled.