Lynne: I've browsed the German pages and it sounds to me like all hosts in Oberammergau issue the electronic guest card right at the inn or hotel - guests are actually charged a small local tax that subsidizes the card. A more select group of hosts offers the Königscard (ker-neeks-cart) (which also covers transport, and which hosts probably charge you for in their standard overnight prices.) Either card will get you the transportation we discussed. As of 8 months ago, certain trains were added to the travel privileges on these cards. For the trains you need the card, your passport, and an official slip of paper your hosts provide.
This page is in German, but it shows the specific TRAIN routes you can also use; travel beyond the last travel points and you will need normal tickets for such travel:
https://www.ammergauer-alpen.de/content/download/25205/328330/version/1/file/BB+Flyer+DB_98x210_din_lang_plus_3mm+Beschnitt_NEU.pdf
The wording in German does not completely confirm that EVERY host offers the electronic guest card. So if it's not clearly included in the host's website materials or at your booking site, in order to be sure, I suggest you just send an email to the establishment and ask.
I suspect that even if a given host does NOT offer this card (and doesn't charge you the tax) that the local tourist office would provide you one for whatever the cost of the tax is (probably €2 or less.) That happened to me once in the Black Forest region where a similar guest card was supposed to be available at every place. Guess I chose a host who was uncooperative with the local tourist office.