This seems to be due to a feature that exists in PHP 5.3 but will cause failure in older versions. For PHP 5.3, they added the ability to omit the 2nd expression in a ternary operator ("var1 ?: var3" vs "var1 ? var2 : var3") in order to return the result of the first expression. This is helpful for some but only when the server is using 5.3 and beyond.
This should probably be changed in order to provide better functionality. I've noticed that there are various things in place to handle previous PHP versions but this single oversight will cause it to fail in anything but 5.3. Hopefully that helps both your issue and the author.
Here's a temporary fix for that line:
$autp_posttypes = ($checkPostTypeSet = isset($this->options['autp_posttypes'])) ? $checkPostTypeSet : null;