OP is saying if you do not update the URL between searches it will not be bookmarkable. Not, if you update the URL with the actual search term in a query string

OP is saying if you do not update the URL between searches it will not be bookmarkable. Not, if you update the URL with the actual search term in a query string. The reason they do not update the URL query string itself is due to browser incompatibility. Doing it this way they get support for all browsers released after 2010, whereas they could only support IE 10 or greater by using History.pushState