Malleable backstories

Human beings are perfectly capable of absorbing stories non-linearly. Very often we meet a person and only later find out about their past. Our experience of them grows and changes over time.

That's the best way to present character backstories, too. We need to see the character behave in the present before we care about how they got to be the way they are. We should only learn about their past once we have a sense of them in the present.

Backstories don't need to be set in stone. Some games let you pick the player's character's backstory, and then will adjust dialogue accordingly. 

But we can also assign characters -- even the player character -- different backstories depending on what the player does. If the game flags that the player likes to rush into combat (not a difficult metric to measure), we can give that player character a backstory that reveals why they are so impetuous, or anxious to prove their bravery. If the player likes to stealth and avoid combat, we can give that player character a backstory appropriate to someone who avoids confrontations. Hopefully that leads to the player feeling a kinship with the character they're inhabiting.