The code is actually https://github.com/readthedocs/sphinx_rtd_theme/blob/master/sphinx_rtd_theme/footer.html#L4

While trying to test this it only takes one tab key to go from one button to the next/

I looked into this again, and verified it works properly when using the tab key to move between the items. However when moving moving between the items with a screenreader, the reader will make an extra stop at a pseudo-element added to the footer using CSS:

.rst-footer-buttons:after,.rst-footer-buttons:before {
    width: 100%;
    display: table;
    content: "";
}

I think if we switch to something like flexbox for the footer and its buttons rather than floats and the workaround above then screen readers will handle it properly.