PHP stylesheet cannot use standard WP functions

If you're linking to a file, it's opened as a new file. So unless you explicitly include wp_load.php or something within that styles file, WordPress is not available.

Loading WP all over again in one page load seems like complete overkill to me. Why don't you just include your style file as an inline stylesheet, if you need to use WP engine?

Do something like this:

<style>
<?php include_once('styles.php'); ?>
</style>

You may consider using some alternative functions to return the path you are looking for instead, for example:

//this one may return as well as some unwatned theme-specific stuff
get_bloginfo('template_directory');

//this returns the pure url
get_bloginfo('template_url');

or

//basically the same as template_directory, may come over with extra info
get_bloginfo('stylesheet_directory');

//returns the url followed by style.css
get_bloginfo('stylesheet_url');

These very well could be subject to the same problem, let me know if this doesn't work. You may have to throw in some includes at the top of your file regardless of what you end up using in order to get any of these to work.

The concept of PHP-driven style sheets is sub-optimal because the PHP interpreter - and the WordPress bootstrap, which is fat! - has to be started for every CSS request.

If possible, consider using relative paths - note that if your style sheet and the image are in the same template directory, things like

../images/image.gif

will work! Paths in style sheets are relative to the actual style sheet's location, not the page's.

Alternatively, while inline styles are indeed bad, consider having a static style sheet, and specifying only the dynamic properties in the document head.

<link rel="stylesheet" href="....." type="text/css">
<style type="text/css">
 .class { background-image: url(<?php echo $xyz; ?>) }
</style>