Why does this Garmin GMA340 have an Airway/Inner marker indicator?
The "A" is not an inner marker. The A is an airway marker. Airway markers were part of a now-obsolete system of "red" airways. They were placed along the enroute path and they could be picked up at cruise altitudes. The red airway system was mostly abandoned in the 60's and few "A" markers are still operational. Here's a map showing where they were located. They weren't at aerodromes. 

Source

The airway markers transmit the same 3000 Hz audio frequency as inner markers so the airway marker can be used to pick up the inner marker. Since you say that unit is not certified for cat II it makes sense that they labeled it "A" instead of "I" although it can be used for inner markers.