Well besides the other games on that list that OP mentioned. I really love a few others (these are all free btw)...
Ib - It's pretty well known by now, but if you haven't played Ib yet you're in for a treat. This game is a fantastic RPG maker survival horror game about a girl trapped inside the painting of a deranged artist, it will break your heart and also there are many different endings.
The Company of Myself - A very fun but sad little logic puzzle game.
One Chance - A very sad little game where they are multiple endings, but true to the title, you have to stay with the ending you get, the very first time you play. There is no replay not even if you reload the page (of course there are ways around this but that misses the point of the mechanic). I recommend really letting yourself get immersed in this one for the best experience.
The End- a long and INCREDIBLY fun game that is mostly a platformer, partly a puzzle game, and all about an intense journey of self. It maps your philosophical profile as you play! How cool is that?
no one has to die. - Just played this one last night, very short and only a bit of puzzle gameplay, it has more to do with story but it's pretty interesting with multiple endings that actually play a role in the narrative.
This Is The Only Level, and it's sequels - This is a bit of a break in theme. Because instead of the plot being the interesting thing, these games play with your expectation of what a game SHOULD be. They will take you by surprise and make you think in different ways.
Achievement Unlocked 1, 2 and 3 - Made by the same guy as above, these games will either entertain you for hours, or frustrate you until you give up, but I love them. Again they play with the user's expectations, challenge the player to think in ways they're not used to, and provide a TON of surprises and even moments of genuine shock. (Psst, 2 is definitely the best of the series.)
Silent Conversation - Is a very soothing and relaxing little platformer (if you need a break from chaos after playing the above games, haha). It has you run along sections of text from poetry and prose. It almost feels like a game a reclusive retired English professor might make (but one with a good eye for game design).
Hero's Adventure - This game is...well, telling you would spoil it. As would reading the comments below it. If you have a faint heart I'd steer clear of this one. It's not a screamer though, don't worry. (Though some rock music does play during battles that is very loud I recommend turning your speakers down a tad).
Peasant's Quest - This game was made by the Homestarrunner crew and it is incredibly fun and silly. It's in the style of old adventure games like King's Quest and it parodies the genre perfectly. In my opinion is the perfect palate cleanser after all the above games and their sadness and dreariness and what-have you. :)