If you click on the link, you find: GNU Affero General Public License v3.0,
GNU General Public License family gpl,
GNU General Public License v2.0 gpl-2.0,
GNU General Public License v3.0 gpl-3.0,
GNU Lesser General Public License family lgpl,
GNU Lesser General Public License v2.1 lgpl-2.1,
GNU Lesser General Public License v3.0 lgpl-3.0.
it takes some searching, but when one selects GPLv3 then the default text does indeed include the "or later" clause.
so not only is it an option, but it is the default option, because an extra step is needed to change that.
unfortunately, in my opinion, the whole choosealicense site could be improved a lot. for example the license templates could be actual form fields letting you fill in the details needed, and then producing a license text that is correctly filled out. as it is, some users will likely miss some fields
obviously he prefers "GPL2 or later" and "GPL3 or later"
does github offer that?