I won't comment on the general game, as others have done so. I will comment on a specific sequence.
Towards the end of the first half, the Chiefs had the ball, up by 3 points with time running out, and were backed up toward their own goal line. The Bills "D" was hoping to force a punt. Turns out after pushing KC back the first two downs, the Bills allowed the first down. (I think by 1 yard, at the near sideline.) So the Chiefs were out of trouble. (I think the Bills forced a turnover after that, further down the field at maybe mid-field, and took a kneel-down to end the half.)
What I want to go back to is the failure to stop the Chiefs on the 3rd down after backing them up on 1st and 2nd. Had the Bills forced a punt, the Bills had a unique opportunity. If they intentionally fair-caught the hypothetical punt (to stop the clock on the change of possession), it may have been a perfect situation to invoke the fair-catch free-kick rule.
The ball must be fair-caught. It cannot be advanced. The subsequent free-kick cannot be attacked or blocked by the defense - they must stay 10 yards beyond the line of scrimmage. A kick holder (2nd player) is used. The down is un-timed, so the kicker can position himself wherever he wishes and take as many steps as he wishes into the kick.
Time clock was running down, which is when you use it - i.e., not enough time to move down the field to attempt a score. If the kick failed I'm 99.99% sure the Chiefs take the ball at the line of the kick. There may have been too much time remaining to attempt such a strategy, but I think it would have been worth the risk. The defense was playing like crap, the Bills had been out-possessed and hadn't been moving the ball well. It would have been an opportunity to tie the game and negate all the woes of the first half on the scoreboard.
I wonder if the Bills coaches are aware of the fair-catch free-kick rule. I guarantee Belichek is.