The issue here seems to be whether the use of a verb telecommute is a sensible way to describe the kind of working that it describes. I am surprised to be writing on this site that whether it is sensible is a question neither of grammar nor of usage. The verb is well-established in the leading dictionaries, with a more-or-less common range of definitions. That means that the lexicographers are satisfied that this word is frequently enough used in a wide enough range of contexts.
With hindsight, it was inevitable that the internet would break many of the remaining controls on the English language. For example, it made it possible overnight to turn nouns like access into verbs, like access: and not just verbs but transitive verbs. Any such ‘rules’ were ‘policed’ by editors, lexicographers and school teachers. We now access the internet and all sorts of apps and opportunities it offers. But this phenomenon is a fact of usage.
The verb to telecommute and its cognate noun telecommuting are fully established. I should add that there seems to me to be a subtlety about their use. I have never heard anyone saying “I am a telecommuter” or “I telecommute”. The words occur discursively, mainly in journals, books and reports related to the discourse of sociology, management, and so-called human relations.
Actual ‘telecommuters’ (and here I have to rely on personal experience) use the term. They more often say that they ‘work from home’. Confusingly, not all people that work from home are telecommuters. Telecommuting implies a base to which you work from home. It is in essence remote working. Moreover, it is not clear that all forms of working ‘from’ home count as telecommuting. For example, for several years I ran a company with an annex office near home, visiting the main office once a week. It is not obvious whether this was a case of ‘telecommuting’ or not. Nor is it clear that by having my PA come to work at my house this would have made any difference.
Commuting itself is a very young idea: less than a hundred years. The term ‘telecommuting’ is still a toddler. Let’s give it a chance to come of age.