It appears their directory solution is custom coded or is run on top of another CMS solution that is not WordPress.
The closest solution available would be similar to the following site in the “Find A Therapist” section
The multiple search is done by using categories in Connections. This multiple category search is actually compatible with all templates. The individual template would have to be configured to turn off their search features.
Currently I do not offer this as an individual item for sale because it is beta (but production ready). Primarily because there is no interface to configure it. I do provide installation and configuration as a service which would be in addition to the purchase your desired template. If you are familiar with WordPress shortcodes and are comfortable using them, if you purchase either the Extension Pro Pack or the Pro pack I will be more than happy to send you a copy to you with instructions on how to configure it.
I hope I have answered your question thoroughly!