You can include **any** file, regardless of the extension. You only need the extension to be .php if you want to execute the code in the include (and even then, I think, it will still execute with inc . . . )
<?php include("textlinks.inc"); ?>
<?php include("textlinks.txt"); ?>
<?php include("textlinks.html"); ?>
<?php include("textlinks"); ?>
Anyway when you do this,
<?php include("textlinks.inc"); ?>
... it means the file textlinks.inc must be on the same server, and in the same directory as the php script including it. Is that the case? Doesn't sound like it:
The table code is in a file located on another site (not one of the 9 sites).
You can try
<?php include("https://www.example.com/textlinks.inc"); ?>
But this will fail if the server is not configured with allow_url_fopen or allow_url_include on - which it's often not by default.
docs [php.net] If these "nine sites" are all located, say, on a dedicated server, you **can** configure them and the sites to open the file regardless of location, but you'll have to use the full server path:
<?php include("/var/www/domainname.com/includes/textlinks.inc"); ?>
If neither of these are possible, your only other option would be to then keep nine copies of the same file on all the sites.