Crossword Puzzle Skip the vote

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They've cleaned up the four theme entries above (STREETSWEEPERS with 14 letters)
Game that's the hidden theme of this puzzle (TICTACTOE with 9 letters)
NYC theater district (BWAY with 4 letters)
Theater space? (ENTRACTE with 8 letters)
Home of the Karl Marx Theater (HAVANA with 6 letters)
Theater mezzanine (LOGE with 4 letters)
N.Y.C. theater award (OBIE with 4 letters)
Whose Â“ThesaurusÂ” is that? (ROGETS with 6 letters)
Thesmothetes' milieus (SENATES with 7 letters)
Thespians' field (ACTING with 6 letters)