Ok...here is what I tried to recreate what you are seeing (if I am doing something incorrect, please tell me). I open Chrome browser (based on your description of the 1 in the box to close the open tab) I click on the same thing; the 1 (or whatever number of tabs open in Chrome) in the box near the upper right hand corner. I swipe away the tab, and I get kicked out of Chrome and go right to my homescreen.
Here is a catch; on my Pixel, if I close all the tabs doing the same procedure, Chrome does not shut down. I have a black screen until I either force open a new tab or I close the Chrome app.