Light can be described either as waves or as particles, depending on what behaviour you want to predict. In the same way, playing squash can be described as either adverbial or participial, depending on whether you want to look at the construction of the clause itself (its head is a participle), or the role of the clause in the complete sentence (it acts as an adverb).
Guidelines about punctuation can be helpful... but you need to use the appropriate guidelines. When considering punctuation of the sentence as a whole, you need to consider the role of the clause in the complete sentence (it acts as an adverb), rather than how the clause is constructed.
The quick and dirty tips link that you provided in your comment about the comma does not seem to be about grammar. The Purdue link that you provided relates to adjectival usages of participle phrases.
Adjectival usages affect just one of the nouns or pronouns in the sentence. This is an adverbial usage, which affects the whole sentence. Here is some advice on punctuation for adverb clauses:
A comma is usually not necessary when the adverb clause follows the main clause.