When people say "homeless" they generally refer to something akin to "not having a place with a roof to sleep in and don't have a choice to have one". If you are staying at a hotel or if you have a home you can go back to abroad you're not considered homeless in that sense.
Who said I had a home abroad? And the hotel was just my longest stay, mostly for medical reasons. My primary accommodation was youth hostels and PGs, which are (materially) more or less homeless shelters.
(Of course they are much higher status. Is this discussion really just about status?)
The premise of gloves' comment (which I'm accepting for the purpose of my comment) is that the person described in the article is also homeless by choice. He certainly seems functional enough to get and hold a job at Chipotle and rent a flat in distant Brooklyn if he wants.
The suggestion is that - much like me - his lifestyle is a choice. Just like you want to compartmentalize my experience with a different label, maybe we should do the same with him and similarly situated folks.
It's at least partly about status. But in the UK one of the possible outcomes of the housing system is a family being accomodated by the council in B&B or hotel accomodation on a "temporary" basis. This is for the very sensible reason that having children sleep on the streets or in homeless shelters is especially bad for their safety and future development. But it can still produce some very weird outcomes, especially when extended for weeks or months.