Like a Dragon Gaiden is just the localized title that was given to this game, the name in Japanese roughly translates to "Yakuza 7 Side Story". As this suggests, this game's story takes place parallel to that of Y7's. Once again we are in control of Kazuma Kiryu, which following the ending of Y6, had abandoned his identity to protect his family. Certain events will start to unfold within the faction he currently serves to, which will point and tie in to a crucial moment in Y7's story. This time around, we get to see the events that transpired from Kiryu's point of view leading into it. Do note that since this title is a "Side story", it is much shorter in all avenues than your average RGG game.
As a return to Kiryu, this game handles as a brawler beat-em-up once more, I've not played the Judgment titles as of yet so I'm not too aware of how the brawling combat improved on the Dragon Engine after Y6/YK2, but in this game it does feel more responsive, Kiryu wields a brand new fighting style, with cold and calculated moves, and Spy-like gadgets to aid in combat. The new style feels good, kind of like a new take of Rush style from 0/K1. The gadgets are interesting but some are very annoying to activate as they require holding down the main combat buttons, perhaps a better method could have been chosen. Additionally there's also a more traditional Yakuza fighting style, with Kiryu's older moves.
The story mostly takes place in Sotenbori, taking the main spotlight for the first time. Since the city itself is not all that big, it fits well the theme of the game and it's more reduced scope, it works perfectly well on my opinion. There's not many changes to the city from previous titles, but there is a new exploration skill using the Spider agent gadget, so there's some extra stuff to seek in town. Besides Sotenbori, you'll also be taken to another area called "The Castle", but this mainly serves as the holding place of the Coliseum and a few select story parts.
Looks like they aimed to have a different Coliseum experience this time around, with a new mode called "Hell Team Rumble", where teams of allies and enemies face each other. This allows even the player to choose different characters to play as for these fights. Unfortunately, every other character besides Kiryu has a very lackluster moveset and is not that great to use. It ends up being more of a grind until your characters are high enough level to crush all fights rather than an engaging mode.
Albeit short, the game is very enjoyable, a lot of the side activities like quests and Sub stories are baked into the main story as an introduction, and they are interesting enough that you can spend several hours just doing them before proceeding with the story. For fellow completionists, I'm happy to report that on this one they didn't actually include too many incredibly grindy tasks, given the smaller scope of the game, the minigames that are included don't entirely require to replay them over and over as much, and for almost all the activities I had a lot of fun doing the requirements.
Of course the game is a must play for everyone who's played all the previous titles and it also serves as a connecting bridge to Yakuza 8, where Kiryu takes a protagonistic role alongside Ichiban Kasuga.