mysql.inc.php was the old (7.6 and below) MySQL driver, while mysqli.inc.php is the new PHP 7.x compatible MySQL driver. Look like mysql.inc.php was removed from the latest ZIP without updating the UPGRADE_CHANGES.txt file.

The following fix should work:
Open install/UPGRADE_CHANGES.txt in an editor and add after line 17:
Code
VERSION-7.7.1:CHANGED: templates/default/newpost.tpl

the following:
Code
VERSION-7.7.1:REMOVED: libs/mysql.inc.php