It's not uniformly irrational or unprofitable to enter a zero sum game. I made a great living for over 5 years playing a zero sum game, and know lots of people who have done it for far longer. Not options trading though. That one in particular I can't speak to.

It's often not that hard to prove within a reasonable certainty that you are a winner (or at least were one), depending on the variance. I haven't looked into the coefficient of variation of options trading though. I might one day.

Also, whether or not something is competitive has nothing to do with whether or not it is a zero sum game. It is generally just a factor of how much money can be made. The software industry is not zero sum, but is highly competitive. Low stakes poker tables are zero sum, but are not competitive at all.