I think it depends on the context, but the short answer is mostly yes.
In a game like I Wanna Be the Guy, there's not really a tone that is established by the difficulty, it is difficult as an extension of old school game difficulty. It's taking that sort of game design and cranking it up to it's logical extreme, to the point where it evokes nostalgia and maybe some absurdity. Hell, the main character is constantly smiling while everything is trying to kill him.
With something like Dark Souls, the difficulty absolutely informs the tone the developers were going for. The narrative is essentially about the end of the world and everything is dying around you. The difficulty of the game (on your first run, anyway) reinforces the hopeless tone, using gameplay to communicate as only games can.
As for difficulty as a barrier of entry, I think a lot of developers worry if their game is too hard because they are thinking of their game more as a product than as a piece of art or creative work. They want that barrier to be as low as possible to sell as many copies as they can. This is certainly true of other mediums, but there are many more examples of difficult works there. There many movies and books that are "difficult" to get through for one reason or another, be it the language used or the concepts they present. Should there be an easy mode for those books or movies? I would argue no.
I wish I could remember who said it, but one of the comments for the similar Jimquisition episode really sums it up for me: "Altering Moby Dick to read like Jack and Jane would destroy the original intent of the work."