I've read The Last Wish and Blood of Elves (very enjoyable, BTW- looking forward to the rest of the translations) and was wondering how much connection there is between those and the game's plot.

Is it an adaptation, or if a brand new story is it set before/after/instead of the books' events?

New story, set five years after events in the last novel (Lady of the Lake).

It is set after the events of the books. I can't say how much the story is connected with the books, because I didn't read them, but there are some characters from the books. Geralt himself doesn't remember any events due to amnesia.

Only read the first book myself, but the princess-monster story is integral to the game's plot (and is very nicely summarized in the opening cinematics).

Let's say... it's a new story and it isn't at the same time.

It's a new story because obviously it begins some years after The Witcher saga as told by the books (starting with The Blood of The Elves and taking four more books). Geralt comes back to life, and find new enemies to fight with new situations.

At the same time, a lot of the situations and even dialogues are directly inspired from the books. i remember clearly some lines (said by Triss Merigold) near the end of the game that were directly taken from the books except that in the books they were said by another character (Yennefer -- that is not even mentioned in the game). It's also obvious that Alvin is a male replica of Cirila in the grand scheme of things.

So yeah, despite being a different story there is definitely a strong connection and when you read the books a lot of what the characters say to Geralt makes more sense. At the same time you may get puzzled by the relationship between Triss and Geralt... Granted, they slept together in the books but only once and she had to use magic to convince him. She had a crush on him but there was no reciprocity -- he considered her a very good friend, that's all. That particularity and the absence of Yennefer left aside, the game is pretty faithful to the books but the books must be regarded as Geralt's past, the past he doesn't remember a thing about.

There's an Inn owner in Chapter 4 (Murky waters) that will tell a story to Geralt (if you ask). This story is the very short version of the books.

Short answer: no it's not an adaptation. It's a whole new adventure for Geralt but very much rooted in the past through dialogues, characters and events.

Extremely informative. Thank you.