The point is that "jugar" can be transitive or intransitive in Spanish, without any change of meaning in the mentioned context.
As a transitive verb, it can be used as follows:
- Ella juega tenis. (Ella lo juega)
In the sentence above, "tenis" is the direct object of transitive "juega".
However, as an intransitive verb "jugar" takes the preposition "a" followed by the article corresponding to the game or sport that follows (el, la). Under (3) in RAE's dictionary, we find in fact this definition and these examples for intransitive "jugar":
- intr. Entretenerse, divertirse tomando parte en uno de los juegos sometidos a reglas, medie o no en él interés. Jugar A la pelota, AL dominó.
I'd also add the plural article, for example: jugar a LAS damas, jugar a LOS dados (play checkers, play dice).
In all of the examples above, "a" + article is the only possible pattern. I think we can only use "jugar" both transitively and intransitively mainly with sports.