Beee on "[Plugin: WP-PageNavi] Issues with mobile design"

I tried it out myself and the answer is yes it does, for me it seems to be working, with some alterations to your code.

step 1.
change all spans to divs in core.php

step 2.
change line 174 of core.php

$out = $before . "<div class='wp-pagenavi'>\n$out\n</div>" . $after;

to

$out = $before . "<div class='wp-pagenavi'>\n$out\n</div><div class='clear'></div>" . $after;

so the rest after won't float.

step 3.
add "float: left;" to .wp-pagenavi a, .wp-pagenavi div {

step 4.
add ".clear { clear: both; }"

That worked for me.