If you are enqueueing your css with wp_enqueue_style, Wordpress will embed the site's url in the style call. Since you defined your site as "localhost", that's what you'll get (even if you access the site using the IP address instead of localhost).
If you are going to access your site from any other machine, defining the site's address as localhost (or 127.0.0.1) wont cut it. You need to use the ip address/domain of your machine, the same one you'll use in the second machine to access the one hosting the wp installation.
E.g.: machine hosting wp is on 192.168.100.103
On the Wamp machine you could add on your hosts file
And on the other machine's hosts file:
Then going to http://site.local in either of them will end up in the same machine.
Since your site is already configured, doing that wouldn't be enough. You need to change the URL in wordpress as well. E.g., in wp-home.php set:
define( 'WP_HOME', 'http://site.local' );
And if you have any content, menus, or anything like that, they'll be pointing to the old URLs. You need to reset them. You could do it by installing wp-cli and doing
wp search-replace localhost site.local --recurse-objects; or you could just install this, and do the search replace in place as well.
Hope it all helps, and that you understand what's going on.