Dear Esther is even less complex - you don't need to pick things up or solve puzzles. All you do is walk and look around you at the beautiful environment, and as you do a sad and poetic story is told in voiceover.
In the case of Heavy Rain and Beyond, you have a few sequences that require you to act quickly, but it's the kind of thing even the most inexperienced gamer could handle.
Do I think these are games? Yes, absolutely. Interactivity distinguishes a game from a movie. But what I find baffling is not the confusion over what counts and what doesn't - it's that I'm not really sure why precisely defining what a game is actually matters.
There are people out there who seem legitimately offended by the existence of these games that "don't count". Those people gnash their teeth in comments about how terrible the game was, about how boring it was, as if a) they were forced to play it, and b) these games, which are often indie titles, are somehow getting in the way of "real games" being made.
To the first point, all I can say is that a little bit of research would save you a lot of time. If you'd played Heavy Rain, or read even a little bit about it and decided it wasn't for you, it would stand to reason that complaining about playing and disliking Beyond is a bit silly. If you know what you're getting yourself into, you won't be disappointed.
It's okay to not be into this kind of game - there are legitimate reasons not to be - but that doesn't mean that everyone who likes those games is stupid and wrong.
And the fact is that these games aren't preventing the next great shooter, or RPG, or racing game, or whatever else counts as a "real" game. Actually, it's the reverse - many creative, less mechanically-driven games have been cancelled because they can't make enough money compared to a first-person shooter. All the existence of these games does is give consumers choice, and choice is a good thing.
And let's play devil's advocate here - maybe we should call them games. It's helpful, I think, to be able to show others outside of the gaming community that these exist. There's still a perception that guns and gore are all video games are, and that's just not true anymore. If you can show a non-believer something a bit different, you might help to change their perception of your hobby.
Ultimately, though, it doesn't matter whether you think something is a "game". Call it a piece of interactive fiction, or interactive video - hell, call it a film with fiddly bits. What matters is whether you enjoy them or not.
If you do, play on. If you don't, play on - just play something else.
* Have you played Heavy Rain, Beyond or Dear Esther? Do you consider them games?