"Les encanta jugar al tenis los sábados."
Translation:They love playing tennis on Saturdays.
Yes, it can be.
Using the "a" after "jugar" depends on the country. If you use "a", you need the definite article as well ("a" + "el (tenis)" = "al").
Why are these verbs like this? Jugar-to play not playing. I don't understand.
'Jugar" is a Spanish infinitive that can be translated as either an English infinitive or an English gerund. However it is important to keep in mind how the -ing word is being used in English. If it's being used as a noun substitute, then it's an English gerund. If it's being used as an adjective, then it's an adjective substitute, which is called a participial.
To suggest that you can write it without "A ellas/ellos" as no need for it but according to DL: "Spanish speakers use this structure even when there's no need for additional clarification"
So both answers are correct