The basic instruction that I can give anyone who watched this anime is, "Play the games. This is an anime for the games. If you watch this anime without playing the games and liking the story, you're screwed."
BlazBlue: Alter Memory is as compressed as can be expected for a series spanning 2 3/4 worth of games' stories (Looking at you, Capcom style additions like "Extend" and "II"). It cut the entire first game of BlazBlue: Calamity Trigger down to about 2 1/2 episodes, which neatly summarized Ragna's "True Ending" in that game. The last 9-10 episodes retells Continuum Shift largely from the perspective of Ragna the Bloodedge, Noel Vermillion, and Jin Kisaragi, making a couple stops now and then to show you:
-What government rebels Kokonoe, Makoto, and Tager have to say about what the main characters are up to,
-What Rachel Alucard thinks of the bullshit caused by Hazama and the government, and
-Big Bad Hazama appearing to demonstrate that he is the worst person ever, and nailing it into your head that he will corrupt Noel's friend Tsubaki Yayoi just for fun.
Now, you may be thinking, "Why didn't they expand upon a lot of the characters? Why wasn't there more screen time for [Character X]? Why didn't they explain more of what was going on with the world? WHAT THE HELL IS A BLAZBLUE AND A MURAKUMO UNIT?!"
I can give you the answer to that: play the games. This story is COMPLETELY INACCESSIBLE WITHOUT PLAYING THE GAMES. Say what you will of adaptations of videogames, but arguably, this story isn't so much an advertising ploy to get people to play the games, NOR is it, in my opinion, a good way to introduce someone to the games. The whole plot essentially exists to be:
1. A FANSERVICE, SOMETHING TO APPEASE PEOPLE WHO ARE ALREADY FANS OF THE GAMES, OF WHICH I AM ASSUREDLY A PART OF.
The scenes showing Ragna's relationship with Noel, Rachel, Taokaka, and Lambda are largely for this purpose: further, the curtness of the fight scenes is arguably there because THEY HAVE 12 EPISODES TO GET THROUGH THE PLOT AND IF THE PLAYERS OF THE GAMES WANTED TO SEE FIGHTS, THEY WOULD PLAY THE GAME. The money of the show is the fun dialogue between the characters whom the player is already familiar with.
(The pinnacle of the above point is the fight between Ragna the Bloodedge and Carl Clover, infamous for being the worst character in the game: the fight lasts for under two minutes and Carl is knocked unconscious by a piece of metal falling on his head, never appearing again in the show).
The only other conclusion that the plot seems to imply is that:
2. THEY REALLY WANT YOU TO PLAY THE UPCOMING GAME CHRONO PHANTASMA TO SEE WHERE THE STORY IS GOING AND GET AN EXPLANATION OF WHAT THE HELL YOU JUST WATCHED.
If that is the case, then BlazBlue: Alter Memory is a cashcow, nothing more, nothing less.
However, the director of the games has stated before that he had always intended to make BlazBlue an anime-- quite frankly, for fans of the games, this anime was the realization of that want, that dream. BlazBlue: Alter Memory is what a BlazBlue fan invested in the main few characters (at least, speaking from my own perspective) could want from an anime. All of the music from the games is re-composed, the scenes in the game are nicely reconstructed, nods are made to certain story paths, and overall, it is a loveletter to those who sat through every route of the game to get the True Ending, in both games.
OVERALL: IF YOU HAVEN'T PLAYED THE GAMES AND YOU'VE WATCHED THIS ANIME, I AM SO SORRY. YOU PROBABLY DIDN'T UNDERSTAND A SINGLE THING THAT WAS GOING ON. BLAZBLUE HAS ADDITIONAL PARTS OF THE GAMES LITERALLY DEDICATED TO EXPLAINING THE LORE OF THE WORLD, AND WITHOUT THOSE BITS, THE WHOLE SHOW WAS LIKELY NONSENSICAL AND RANDOM.
To watch BlazBlue without playing the games is to watch one of the Harry Potter movies towards the end of their run: you have no context, and thus you'll likely have no fun. However, IF YOU LIKE BLAZBLUE'S STORY AND CHARACTERS, THIS ANIME IS BEAUTIFUL AND IT WILL MAKE YOU HAPPY.
To those who criticize the story for being random and incomprehensible, YOU NEED A LOT OF CONTEXT FOR THIS STORY. To help amend this, THERE WAS A WEBSITE THAT LISTED ALL THE INFORMATION ABOUT THE LORE TO ASSIST YOU. However, it was in Japanese and likely didn't explain enough. Furthermore, COMPRESSING SUCH A COMPLICATED PLOT INTO SUCH A SHORT AMOUNT OF TIME LEFT NO TIME TO EXPLAIN TO THOSE WHO DIDN'T ALREADY UNDERSTAND.
IF WE WERE GIVEN A LONGER ADAPTATION, WE COULD'VE HAD FLASHBACK EPISODES TO EXPLAIN WHY EVERYONE WAS SO ANGRY ALL THE TIME, BUT UNFORTUNATELY, THAT WAS NOT THE CASE, AND THUS, THIS ANIME IS REALLY JUST FOR PEOPLE WHO ALREADY LIKE AND UNDERSTAND THE GAMES.
Final Score for Non-fans: 6.5/10, You'll be confused.
Final Score for Fans: 9/10, It's a dream come true.