Goats at Nugget Falls on February 9, 2017 | Bob Armstrong's Nature Alaska

Goats at Nugget Falls on February 9, 2017 shows several clips of them feeding.
It seems fairly obvious that they were eating lichens, moss, and alder but not sure what the brush like vegetation was.
To learn about their ability to use lichens as food look at this essay by Mary Willson
For good information on Mountain Goats in Southeast Alaska look at Relation Between Mountain Goats and Their Habitat in Southeastern Alaska by Joseph L. Fox, Christian A. Smith, and John W. Schoen