$this_is_home_page is a special case; it's not done for other pages.

If you want to check the name of the current page you can do so using the variable $current_page_base.

if ($current_page_base == 'shopping_cart') {
...
}

if ($current_page_base == 'product_info') {
...
}

but if all you're doing is adding page-specific CSS, you'd be better off doing it the way I suggested; that way you can upgrade your template at any time and not lose these customizations.