Sword Art Online or SAO for short is by no means a perfect anime. It has many faults and trips into many pitfalls that a lot of shows also fall in. The second series (or season depending on whom you ask): SAO 2 left much to be desired. But the fact that it's well-known cannot be disputed. Sword Art Online Alternative: Gun Gale Online is a spinoff series within the realm of SAO. (as its title would suggest)
As with any spinoff, the series follows a new protagonist: Karen Kohiruimaki known better as her online handle LLEN. Even if you're unfamiliar with SAO or SAO 2 you can watch this series without being lost. It touches upon the events in SAO without knowing everything about it being necessary. This allows the show to stand on its own two feet; the fact that it follows a new hero addresses a problem that the original show had, being that it focused entirely too much on the main character and had him being overpowered throughout the series.
A few warnings about the show. It contains scenes of somewhat graphic violence throughout, but it's pixelated so you don't see guts flying about but there is something akin to blood. It has mentions of suicide and there are guns being fired throughout.
In this series, Karen Kohiruimaki has gained fame as "the Pink Devil" being a player killer in Gun Gale Online (GGO); a "full dive" VR based game in which the gear allows the player to control their avatar as if it were really them. One day while playing she comes across Pitohui (named after a poisonous bird), a particularly strong female player. The two become friends, as there aren't many female players in GGO, and as they spend more time together LLEN starts to notice some red flags about Pitohui.
But it becomes much more clear during a team tournament called Squad Jam when she's paired up with another player who knows Pitohui in real life, the player simply known as M lets LLEN know that Pitohui is obsessed with the idea of a game you can really die in. Had M been killed in Squad Jam, she would kill him in real life. Though they win the tournament, Pitohui isn't satisfied since she couldn't participate. Our hero learns that at the second Squad Jam, Pitohui will kill herself should she be killed by anybody but LLEN. Not knowing who Pitohui is in real life, in order to save her life, LLEN has no other choice but to enter Squad Jam and kill her.
The show is a far stretch from perfect, but it certainly makes quite a few strides where the original series couldn't. The first being that it has interesting female characters. The original series had female characters but they were two-dimensional (personality-wise) and most of them were just props for the main character. (who was bland himself) Sword Art Online Alternative (SAOA) has female characters (a lot actually now that I think about it) with actual personalities and lives of their own outside of what the main character does. For that alone, I would say it's better than the original.
There's also the villain: Pitohui. She's far more interesting than the past villains the series has had. She's far more active than her predecessors and a lot less creepy. One can argue that she's not actually a villain and but just the antagonist of the show. Though villain and antagonist are often associated with each other, they aren't the same. In the case of this show, Pitohui may have the looks and demeanor of a villain, but she is more a victim of her mental state than anything else.
Wanting to feel alive is the reason why she threatens to take her life over a game, that doesn't excuse her behavior but one can question if that makes her a villain. In order to be a villain, a character must actively plot and take measures to stop the hero from ruining the said plot. Had Pitohui truly wanted to die, she'd just do it instead she gambles it on the outcome of the tournament.
Whether this show makes a positive or negative message regarding mental health is for someone more qualified than I. But it definitely brings a positive one about friendship and helping others. The lengths Karen goes to help save a friend she's never actually met are impressive (though she did have to kill her to save her).
The show also touches upon the healthy escapism that video games can provide. The main character Karen Kohiruimaki is a very tall woman, she towers over men and women and she's very self-conscious about it. The avatars that the games give are randomized and GGO gave her a short, cute one which is why she loves it so much. It gives her the chance to be someone other than herself for a while, which is something I think everyone can relate to. There's also the stress release that video games have but expressing it via shooting people is a little less relatable.
All in all, the show has improved my view of SAO as a whole and the "video-game anime" trope which to me has a lot of potential but is so often wasted on boring main characters without the slightest hint of personality. Sure, it being a spinoff of SAO it could've gone anywhere (game genre-wise) and it choosing an FPS is a little disappointing, but the plot and characters make up for it. It has 12 episodes, for now, and can be found on Crunchyroll. (or whatever site you use) I hope you enjoy it!