Not sure the 2nd period stats are accurate. For example, right now the IIHF says Brink also played 0 minutes in the 2nd, which definitely isn't true as he was the one that created the play at the end of the period that Pinto buried after the buzzer. That's not to defend the TOI distribution at all, but these tweets are likely wrong.
Box score says Kaliyev played 10:05 total, which would almost be 8 minutes in the 3rd if he didn't play in the 2nd, which definitely isn't right, so he must have played some in the 2nd.
Edit: yep, I was right. Kaliyev played 4:14 in the 2nd. You'd think a Kings writer watching for 2 players would have noticed.