There used to be a category of "Outstanding Individual Performance in a Variety or Music Program". This category was around from the early 80's to a few years ago.
1982-Nell Carter and Andre DeShields won Emmys for their performances in Ain't Misbehavin
1985-George Hearn won for Sweeney Todd
2004-Elaine Stritch won for Elaine Stritch at Liberty
2005-Whoopi Goldberg-nomination for Whoopi Back to Broadway
2003-Robins Williams-nomination for Live on Broadway
1993 -Lily Tomlin-nomination for The Search for ....
1985-Angela Lansbury- nomination for Sweeney Todd
Before this category and currently they were put in the Movies/Limited Series categories:
Category was "Best Single Perfomance:
1955-Mary Martin won for Peter Pan
1957 Julie Andrews was nominated for Cinderella
There are also several nominations in the 50's and 60's for classic Broadway Plays (i.e. The Crucible, The Miracle Worker, MacBeth, etc) I am not old enough to know if these were filmed versions of the stage plays or a movie version. I do know that they had several filmed versions of stage plays during this time. Much like the Peter Pan and Cinderella productions.