It turns out that, although the status of several might be disputed, roughly 1/5 of the non-documentary films on the previous list have elements of fantasy, science fiction, or horror to them.

8.134 Inside Out (2015; imdb)
8.118 Song Of The Sea (2014; imdb)
8.100 The Tale of the Princess Kaguya (2013; imdb)
7.857 Mad Max: Fury Road (2015; imdb)
7.776 Harry Potter and the Deathly Hallows: Part 2 (2011; imdb)
7.728 Star Wars: Episode VII - The Force Awakens (2015; imdb)
7.566 Gravity (2013; imdb)
7.520 Her (2013; imdb)
7.488 The LEGO Movie (2014; imdb)
7.452 The Martian (2015; imdb)
7.452 Marvel's The Avengers (2012; imdb)
7.395 The Dark Knight Rises (2012; imdb)
7.371 Guardians of the Galaxy (2014; imdb)
7.296 What We Do In The Shadows (2014; imdb)
7.280 X-Men: Days of Future Past (2014; imdb)
7.189 How to Train Your Dragon 2 (2014; imdb)
7.144 Hugo (2011; imdb)
7.110 Live Die Repeat: Edge of Tomorrow (2014; imdb)
7.084 Ex Machina (2015; imdb)
7.031 Big Hero 6 (2014; imdb)
7.020 When Marnie Was There (2014; imdb)
6.956 The History Of Future Folk (2012; imdb)
6.942 Captain America: The Winter Soldier (2014; imdb)
6.900 Source Code (2011; imdb)
6.882 Looper (2012; imdb)
6.840 Dawn Of The Planet Of The Apes (2014; imdb)
6.786 Star Trek Into Darkness (2013; imdb)
6.786 X-Men: First Class (2011; imdb)
6.764 The Hunger Games: Catching Fire (2013; imdb)
6.764 Frozen (2013; imdb)
6.708 Wreck-it Ralph (2012; imdb)
6.693 It Follows (2014; imdb)
6.674 The Rabbi's Cat (2011; imdb)
6.664 The Babadook (2014; imdb)
6.660 The Witch (2015; imdb)
6.650 A Girl Walks Home Alone at Night (2014; imdb)
6.650 Snowpiercer (2013; imdb)
6.624 The Lobster (2015; imdb)
6.596 Housebound (2014; imdb)
6.461 Holy Motors (2012; imdb)
6.450 The Conjuring (2013; imdb)
6.440 The Cabin in the Woods (2012; imdb)
6.324 Journey To The West (2013; imdb)
6.319 Bone Tomahawk (2015; imdb)
6.248 Coherence (2013; imdb)
6.232 Rise of the Planet of the Apes (2011; imdb)
6.230 The World's End (2013; imdb)
6.216 Predestination (2014; imdb)
6.132 The Hunger Games (2012; imdb)
6.120 Fullmetal Alchemist: The Sacred Star of Milos (2011; imdb)
6.106 Interstellar (2014; imdb)
6.106 Robot & Frank (2012; imdb)
6.090 ParaNorman (2012; imdb)
6.090 Frankenweenie (2012; imdb)
6.072 White God (2014; imdb)
6.035 Chronicle (2012; imdb)
6.030 Spring (2014; imdb)
6.016 The Survivalist (2015; imdb)
6.004 Dragon Ball Z: Resurrection 'F' (2015; imdb)