Swiping browser tabs is not a tablet feature since you always have the tabs available with the "X". This is only available on the phone version since you don't have tabs at the top of the page.
From the change log: Swipe to dismiss notifications, tasks, and browser tabs
You can now dismiss browser tabs and individual notifications and apps from the Recent Apps list, with a finger swipe motion.
To make sure we are talking about the same thing; the "recent activities" list is brought up by hitting an icon on the lower left side of the screen (two overlapping rectangles). This action brings to the screen a vertical display of thumbnails showing screen images of recently opened apps that are running in the background. Touching a thumbnail, and swiping to the left (to the right I did not try) removes the app from the list (I assume that closes the app).
I also assume this is what the "Close by swiping" feature is.
It seems to be on some web sites but not others. It does not seem to stick on sites like the verge, but other sites seem to stay in desktop mode, at least until a restart. This is one of the features I have been somewhat disappointed in, hopefully it will get better in time.
there is a checkbox for requesting the desktop version on the browser settings dropdown (top right), but you have to recheck it everytime you open the browser. Easier than typing about debug, but still not sticky.