I've played Depression Quest, and I didn't see it as particularly good. It's okay; it captures what having depression is like to an extent and the visual and sound design were pretty cool, as was the feature of crossing out certain options depending on the player character's emotional state in order to drive home how depression can cripple its sufferers to the point that they're virtually incapable of certain normal things. But it's rather generic and, speaking as a depressive myself, it isn't realistic enough on its topic and doesn't really go deep enough into its exploration of depression.
I haven't played Gone Home, but I've seen playthroughs of it and it doesn't seem particularly bad. The story is not particularly great: it's essentially a generic coming-of-age story that's been repeated dozens of times in young adult literature. But the framing of a graphic adventure game is certainly interesting, and the way the gameplay functions primarily as a means of exposition is certainly a good idea.
However, they've come under attack for various reasons. But the reason that bothers me the most is that they're 'not games'.
And why does that bother me? Because these allegations are patently false, and their intent is primarily to denigrate them without addressing them on their own merits.
So why, exactly, are they games? What is it that makes them games, as opposed to simply pieces of interactive software?
To start with, Depression Quest, when it comes down to it, is a text adventure. The choices you make while playing it affect certain variables and lead to multiple endings. Although you're limited to a certain amount of choices, this is not unique among text adventures. Prompt-based text adventures, which require the player to type in commands, still have this type of constraint, although instead of simply presenting a list of options, an unrecognised command prompts a response along the lines of 'I didn't understand your command'. To say that Depression Quest is not a game is to dismiss Zork, Curses, and even Steins;Gate, a visual novel which similarly only has text-based choices as its gameplay, as non-games.
As for Gone Home, it is a graphic adventure game. Although it contains no puzzles, its primary focus is on uncovering the story. This makes it what is known as an exploration game, in which exploration and atmosphere are integral parts of the gameplay. Yet this is at the root of what makes people accuse it of 'not being a game'. Kentucky Route Zero, a game which similarly has no puzzles or challenges, had its first two episodes released the same year as Gone Home was, yet I haven't heard any complaints that it's 'not a game'. (This is why I suspect political motivation in these accusations: an exploration-based game without puzzles or challenges but isn't an 'SJW game' (whatever that means) receives few to no accusations that it's 'not a game', but an exploration-based game without puzzles or challenges yet has LGBTQ+ themes receives a lot of accusations of that sort.)
Roger Ebert defined what, to him, distinguishes video games from art in one of many highly controversial essays:
One obvious difference between art and games is that you can win a game. It has rules, points, objectives, and an outcome. Santiago might cite a[n] immersive game without points or rules, but I would say then it ceases to be a game and becomes a representation of a story, a novel, a play, dance, a film. Those are things you cannot win; you can only experience them.
By this definition, Depression Quest would be a game, but Gone Home would not. Yet I would dispute a certain part of his definition: namely, that there must be points and objectives.
Telltale's episodic game The Walking Dead, based on the comic series by Robert Kirkman and Tony Moore and inspired by the success of its television adaptation, received universal acclaim from critics and players alike. It received over 80 Game of the Year awards among many more awards. Metacritic, which aggregates game reviews, gave the Xbox 360 version a rating of 92/100, the PlayStation 3 version 94/100, the PC version 89/100, and the PlayStation Vita version 82/100, adding up to a total average of 89.25/100. Steam users, a good enough representative sample of gamers, rated the game 'Overwhelmingly Positive' based on an aggregate of 26,274 user reviews, only 4% of which were negative. I've played it twice and loved it each time.
And yet there are arguably no points or objectives in the game. There are occasional puzzles which have to be solved in order to progress in the game, but they're heavily de-emphasised. Each episode has five moments in which the player must make a crucial decision between two options—when you think about it, a very similar game mechanic to Depression Quest—which dramatically alters the course of the game. There are also conversations in which the player is given a limited amount of time to choose which response to say, which can have a major impact on how the other characters feel about the player character, Lee. There are quick-time events in which the player must keep Lee or other characters alive; sometimes, these quick-time events require the player to choose which of two major characters to keep alive. But unlike in other games, in which the choices made result in rewards or punishments for the player, there is nothing of that sort in The Walking Dead. The results of each choice are ambiguous: there are no 'win' or 'loss' conditions. The only purpose of the player's decisions is for the player to see how the story unfolds. There are rules by which one must play and there are outcomes of the player's decisions, but there are no points (unless by 'point', one means 'purpose') or objectives.
And no one that I know of has claimed that The Walking Dead isn't a game.
Gone Home has rules and an outcome, although it has no points or objectives. Depression Quest has rules, points, multiple outcomes, and even, arguably, objectives—that is, to reduce the player character's level of depression, to get them into therapy, and to get them on medication.
So both Depression Quest and Gone Home are games. Feel free to dislike them—I don't see them as particularly great—or even hate them. Call them 'SJW games' or dismiss them entirely. But don't say they aren't games unless you're willing to present your case as to why.