I have a little experience with viewing bullet projectile damage from target practicing with various objects.
IMO I do think that is bullet damage. It almost looks to me that the bullet went straight at the edge which would cause damage to both the upper and lower sides of the seat part. I hope LE has looked inside that damaged area because the lead or copper jacketed projectile could still be embedded inside the chair if it went in straight at the edge like I suspect.
There is more damage to the top part where it splintered upwards so if I am right that its bullet damage then the bullet could have come out the top. But even so there could be small pieces of the bullet inside that wood.
LE probably was able to get other bullets from the scene so they may not need to recover it.
Expanding on this. If it was bullet damage then I have to wonder if maybe the chair had gotten knocked over and as the perp shot downward at one of the victims the bullet may have gone downward toward the edge of the chair like that if the chair was already knocked over.
Or as was mentioned by others the chair may have been used as a shield when someone was pointing a gun at them.
this is also a good possibility either way i think its bullet damage and the bullet is likely in the chair.
re the splintering is something the happens in wood due the the nature of the material is fibrous it breaks along weak points and cause splintering.