Follow the instructions here:

http://kb.mailchimp.com/campaigns/images-videos-files/add-video-to-a-campaign

Use the unique video ID at the end of any of your videos to create the Mailchimp embed video tag.

Video:
https://fwd4.wistia.com/medias/XXXXXXXX

Becomes this in Mailchimp:
*|SERVICE:[$vid= XXXXXXXX]|*

The other settings you see are optional.

*|SERVICE:[$vid= XXXXXXXX, $max_width=300, $watch_url=https://fwd4.wistia.com/medias/XXXXXXXX, $trim_border=N]|*