Can I allow that handler to only run on sub-domains to stop PHP parsing on them sub-domains? I still host a vBulletin forum on the same server - so, of course, I don't want to stop PHP altogether.

place it in the sub-domain container <virtualhost> subdomain </virtualhost>

Depends on how your PHP is set. If you run it via CGI or FastCGI - usually you've an Suexec Wrapper - something like:

Global HTTP Conf:

And then place in your Vhosts:

Using this you've PHP running under different users for each Vhost. If that line is missing, no PHP will be executed.
Just look how you can set FastCGI with an Suexec Wrapper.

If you use the Module:

Will do it. The second one isn't required, just to be safe setting open_basedir to a non existing directory never hurts.
Or you do it vise versa and disable PHP globally by php.ini then enabling it only for the Vhosts you will need it. :)

He is using a cpanel server, those instructions will not help him to put it in the needed location.

Someone else might not using cpanel so these instructions might be still useful

I didn't state they wasn't useful, i only stated that they won't work on a cpanel server, which he is using.