These Unique IDs are used when composing profile update and
unsubscribe links, so it's not really a good idea to pass it out to
other subscribers. (It's not clear if you were planning to or not, but
here it is just in case). Either way, listMemberInfo does provide this
UniqueID, although it may not be the most efficient way to calculate a
random winner.
Instead, it would be better to export the subscribers with the Export
API (unless they're already in your DB), and just rand[list_size] on
this dataset to pick a random subscriber and get their email address.
Email addresses are unique to a list, like the UniqueID. So for either
an internal "come to our store and tell us your address to see if you
won" or a "winning announcement campaign", using their email address
would be just as effective.
If wanting to announce the winner by campaign, then a campaign could
be customized with conditional merge tags to display the proper
content to the winner and losers, as described here:
http://blog.mailchimp.com/using-conditional-merge-tags-for-prizes/