There's a bug on the web version where restarting from checkpoint disables all dialogue and cutscenes softlocking you when you get to the boss
Viewing post in Starbreed [3D Rail Shooter] comments
Ah, yes it seems to be a bug that's been around for a while (Some people say if they "Reload from checkpoint" again, it seems to fix it.). I have been looking into it, but have yet to find the cause. Thanks for the report!
*EDIT* - I did end up finding the cause, and will be fixed in future versions of the game.