AWPCP has supported this since v. 3.0. You must follow the WordPress video embedding rules (these are not controlled by AWPCP in any way–only certain sources of videos are allowed (whitelisted) by WordPress and only certain formats of embedding are allowed as well). For example, you can’t use iframes in this context.
In addition to this, you must turn on “Allow WordPress Shortcodes in Single Ad page layout”, which enables you to use shortcodes in the Description field to place the video. You can find this option under Classified Admin > Display > Layout and Presentation, as shown below: