So Andorra is setting itself apart by ensuring that Andorran Euro coins actually circulate
Not really - all monetary agreements (since ~2010) have similar conditions, with a somewhat lower "at face" portion for the Vatican.
* Andorra - Article 5 (2): "At least 80 % of euro coins intended for circulation shall be put into circulation at face value."
* Monaco - Article 6 (4): "Without prejudice to the issuance of collector coins, at least 80 % of euro coins intended for circulation shall be put into circulation at face value each year by the Principality of Monaco."
* San Marino - Article 5 (3): "At least 70 % of euro coins intended for circulation shall be put into circulation at face value as of the year following the entry into force of this Agreement."
* Vatican - Article 6 (4): "Without prejudice to the issuance of collector coins, the Vatican City State shall put in circulation at face value at least 51 % of the euro coins issued each year."
Of course that does not mean that all pieces are issued at face. :) The Vatican for example has issued about 8 million 50 cent coins at face since 2010; the other denominations come in sets.
By the way, the designs you show are different from the final designs. The Numismática Visual article in your link has the ones that will be minted. Also, do not expect those pieces to be issued on New Year's Day. After all, Andorra already uses the euro; these coins will probably come some time in the first quarter. Latvia on the other hand will actually switch from the lats to the euro on 1-Jan. You can already get starter kits there ...