What Does the Dragon Say? We Don't Know
Yep. Not a single one in cut scenes. I first saw this in a Kotaku live play through on Facebook and it was jarring. Remarking after the initial sequence that the players would go into the menu and turn on subtitles, they were shocked to find that no option was available. All cut scenes are voices only with no written dialogue to accompany them. If you're in the over-world there is on screen text when interacting with characters for Spyro 2 and Spyro 3, but that's the extent of the content. Main story sequences are not subtitled. If you're a deaf gamer or have hearing problems, this is an issue. The game is blocking you from enjoying it due to your medical condition. Yes, you can still fly around and breathe fire, but without context of the story, is it as enjoyable?
The initial response from Activision is best characterized as dismissive. There is "no industry standard for subtitles." Followed by a note that they wanted to keep the game as close to the core product as possible. There were no subtitles in the first game, therefore there are no subtitles in this version.
But it's 2018. Gamers come from a wide variety of backgrounds. What was acceptable in the 90's for functionality and accessibility does not work today. We expect all games, even remakes, to have subtitles.
Activision has revised their response and will look into possibly patching in subtitles. As of now there is no guarantee that they will do it, or an estimated time frame on when this will happen. But it's important for all developers to remember that accessibility matters. Dropping subtitles is a quick way to earn our ire.