"De la/of the" implies ownership, as in "el perro de la chica"="the girl's dog". While DL's literal translation "the best player of the league" is awkward, "the league's best player" is natural English and accurate.
Some more cheats: el ama de casa (the housewife) el asma (asthma) el arca (the ark) el hambre (hunger) el hampa (the underworld) el arpa (the harp) el águila (the eagle) http://spanish.about.com/od/adjectives/a/el_for_la.htm Your point about "el" when referring to people is a good one though. Escpecially when several occupations such as "artista", "dentista", or "modelo" do not change endings for gender, so gender is instead defined by the article.
My opinion is that it would mostly likely be said, "He was the league's best player".
(I will note that I am not confident this is one of DL's accepted answers, because I was not willing to risk it.)
I think this works in response to a question like "Who took that half court shot at the buzzer?" You could say "It was John", or "It was the the best player of the league" if you're not into the whole brevity thing.
I put "she was the best player in the league" but was marked wrong because I didn't use the work "he." I thought fue was gender neutral unless el or ella preceded it.
Nothing wrong with it. Probably only because they chose, in the English translation above to write "he".
Yes, "fue" could refer to "he" or "she", but if the gender of the player is known, as it is here, then "jugador/a" must match that gender. If the gender is unknown then "jugador" would be used. So, in a mixed gender league you might ask / answer:
¿Quién fue el mejor jugador de la liga?
[El] Fue el mejor jugador de la liga.
[Ella] Fue el mejor jugadora de la liga.
I guess it comes down to context.
[In 2017] He was the best player in the league - [En 2017] Fue el mejor jugador de la liga.
[When he was young] He was the best player in the league - [Cuando era joven] Era el mejor jugador de la liga.
Out of context the imperfect jumps into my mind too, but either form should be acceptable based on the English.