My argument is, from the eyes of the website you visit, the Steam Deck user would be identified as a desktop user. That's because the browser you are using (most likely Firefox) and the desktop environment (most likely KDE) in the Desktop mode would be seen as a desktop. In short, yes, I think Steam Deck would be counted, but only if people visit the pages in Desktop mode. So not all Steam Deck users are counted here.
Game mode doesn't have a browser. I would be interested to find out of the steamdeck sales almost directly correlate to this increase. Not that I am complaining, it's a great way to use a linux desktop experience. I didn't really read how these numbers were measured.
The other explanation I could think of is that linux desktop is being adopted widely in India. I don't think that government's adopting linux desktop accounts for a significant portion of the machines.
My work laptop is windows and I hardly use it for anything personal. I just unplug the usb-c dock from it and plug it into my steam deck and use it as my desktop. I've done everything with it you can do on a computer.