Last Day of June was also a lovely and emotional experience for me. I hope you'll enjoy it as well!
Patient Gamers
A gaming community free from the hype and oversaturation of current releases, catering to gamers who wait at least 12 months after release to play a game. Whether it's price, waiting for bugs/issues to be patched, DLC to be released, don't meet the system requirements, or just haven't had the time to keep up with the latest releases.
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They probably aren't your cup of tea but thought I'd add some more variety.
Final Fantasy XIV; an mmo with focus on story and the story arc from the past 9 years is wrapped up and brought me lots of tears.
Honkai Impact 3rd; ARPG gacha game (I know, I was skeptical) also with years of story following a relatively small cast of characters.
Yakuza Zero has a story that is excellent, albeit goofy at times. In the end, it got me good.
The Yakuza series beyond Zero is also bloody amazing.
One moment you're laughing your ass off and the next thing you know you're in emotional anguish. If you're okay with Japanese weirdness (oh trust me it gets really weird), this series is a great rabbit hole to get into
The most recent one to make me cry was...
"I Was a Teenage Exocolonist"
Probably gonna get hate for it but I'm a man in my 40's and some of the Genshin Impact story lines have left me in tears.
One I've not seen mentioned but made me bawl my eyes out is 'Presentable Liberty' Im not sure about the remake, but the original was pretty short and was gripping, despite the low level of action.
People already recommended some Final Fantasies, but really all of them can get you quite emotional at times.
If you like VNs, Umineko no Naku Koro ni made me cry so many times...
Edit: Just remembered Once on a Windswept Night, it's just a short game you can complete in a hour, but for some reason it made me really emotional.
Lisa: the Painful
I dont know if its listed here yet.
God of War: Ragnarok got me close to bawling. Father son moments always get me in movies and games, and this was one of the best.
I still need to play the first (rebooted) one. Also I game on PC, so I gotta wait for Sony to give the OK to the devs to port it over like they did woth the first one.
If you've ever experienced grief, then Gris. I still listen to the beautiful soundtrack regularly
Les Soldats Inconnus
Golf club wasteland made me cry. It's a quick game, but I found it very touching.