The -ing forms in this sentence are not used as components of tensed verbs in the continuous construction but as nouns, objects of the preposition for.
Our kids needed athletic shoes.
What did they need them for?
They needed them for playing outside and for participating in gym class.
When an -ing form is used this way, as a noun, it is called a gerund. Gerunds act like both nouns and verbs. As verbs they take subjects and objects and are modified by adverbials; but as nouns they (or the clauses which they head) may serve as subjects or objects in a clause or as objects of prepositions.
Swimming is fun. .. In this sentence the gerund swimming is the subject.
Playing football is fun. ... In this sentence, the gerund playing takes the object football, but the gerund phrase playing football is the subject of the sentence. (In traditional grammar, the gerund playing would be regarded as the subject, but that is a minor detail).
We need a ball for playing football. .. In this sentence the gerund phrase playing football (or the gerund playing) is the object of the preposition for.