I have a... System.
I see a game that looks interesting enough that I am willing to load the games description. Usually the artwork speaks to me, maybe I recognize the author, regardless that's enough for me to open the games description. Once I have committed to opening it, I have a giant spreadsheet that I use to track all the games I have shown at least that much interest in. The spreadsheet has the game name, author, several (subjective and numerical) ratings regarding how much I enjoyed the game, whether I think I'd like to return to review it at a later time, how good the artwork, story, humor, etc was. Also a small description area where I put any notes if I feel like it and also a link to where I downloaded it. If I have no record of it, I create the record and rate the artwork in the previews. If I do have a record I remind myself of whether it's worth downloading for the new content based upon its rating and how likely I felt I'd like to return to it when originally rated it.
Once I read the description, I might choose to download the file. I place the unzipped file on my desktop. I play it, the very very very beginning of the game gets saved in a specific save spot so that I can come back and reread the plot later if I can't remember it.
Once I have played it enough to evaluate it, I then rate it and record that info in the spreadsheet. If I liked it, I save it on my 2TB game drive with an amended naming convention that includes the overall rating I gave it. If it's average I'll probably play it enough to get bored of it and delete it. If I don't like it, I delete it.
So, for the actual question. If I need a refresher on the plot, I can reread the games opening and my notes. If I did not actually like the game, I am really unlikely to return to it later. But If I do return and can't remember the story, I'll start over until it rings a bell and then decide if I want to start over or load my most recent save file (also in a specific save spot).
But the reality is that most games are either fresh enough in my memory that the new update is just another chapter in a continuing story I am reading (In for a penny, Crimson High, Single Again, Light of my life, Fall of the Angels, A foreign World, Out of Touch, The Big Step), or it is low enough stakes in my mind that it isn't important enough to refresh my memory (The Button, Goblin Gnight, Hardstuck, Out of Puberty, Adored by the devil, Powers that Be, Grandmas house). If I find I can't easily remind myself of why I was playing it, I likely rated it too highly, or it's a convoluted sandbox game.