It begs the question... if "released theatrically" is a necessary qualification, then shouldn't you only count movies that you saw in a theater? Otherwise, why is that an important rule for what defines a movie?
...and then that makes me wonder what my top 250 would look like if I restricted it to movies I saw in a theater. It would be a whole lot different. I could still include Fanny & Alexander, but would it have to be the theatrical version?
The only films from my list I've seen in a theater:
8. Alien (1979, Ridley Scott)
27. The Black Stallion (1979, Carroll Ballard)
33. Boogie Nights (1997, Paul Thomas Anderson)
42. Close Encounters of the Third Kind (1977, Steven Spielberg)
57. Do the Right Thing (1989, Spike Lee)
64. The Empire Strikes Back (1980, Irvin Kershner)
71. Fanny and Alexander (1982, Ingmar Bergman)
72. Fantastic Mr. Fox (2009, Wes Anderson)
73. Fargo (1996, Joel and Ethan Coen)
79. Gimme the Loot (2012, Adam Leon)
82. Glengarry Glen Ross (1992, James Foley)
89. Harry Potter and the Prisoner of Azkaban (2004, Alfonso Cuaron)
101. Indiana Jones and the Last Crusade (1989, Steven Spielberg)
104. It’s a Wonderful Life (1946, Frank Capra)
121. The Lord of the Rings: The Two Towers (2002, Peter Jackson)
132. Midnight Run (1988, Martin Brest)
163. Pink Floyd: The Wall (1982, Alan Parker)
166. Raiders of the Lost Ark (1981, Steven Spielberg)
175. The Royal Tenenbaums (2001, Wes Anderson)
176. Safe (1995, Todd Haynes)
190. Silent Hill (2006, Christophe Gans)
And a few of these I'm not entirely sure of.