TL;DR: the good divisional record (at worst 4-2) and excellent conference record for the Chiefs (at worst 9-3) means that they win the tiebreakers over the other relevant teams (Broncos, Jets and Steelers).
How the Broncos can miss the playoffs
The Broncos lose to both the Bengals and the Chargers, while the Chiefs beat the Raiders. The Chiefs win the AFC West with an 11-5 record, while the Broncos are in the wild card mix with a 10-6 record.
At this point, the other important teams are the Jets and the Steelers. The "worst case" scenario for the Broncos is both the Jets and the Steelers winning; in this case, the Jets have an 11-5 record and claim the first wild card spot. The Steelers have the same 10-6 record as the Broncos, but claim the second wild card spot on the basis of their better conference record (7-5 vs 6-6).
Why the Chiefs always make the playoffs
If the Chiefs win their final match, they are 11-5. At this point, they are either AFC West champions or guaranteed to have one of the two best records of non-champions (the only other non-champion which can possibly get to 11-5 is the Jets), so they are guaranteed a playoff spot.
If the Chiefs lose their final match against the Raiders, they have a 10-6 record. If the Broncos have lost their final two matches, the Chiefs are AFC West champions on the basis of their better divisional record (4-2 vs 3-3) as the Broncos and Chiefs split their two matches this year.
If the Broncos win one of their final two matches, they are 11-5 and AFC West champions, while the Chiefs are in the wild card mix. The important teams are once again the Jets and the Steelers - if they both win, the Jets again claim the first wild card spot at 11-5, and the Steelers are at 10-6. The Chiefs win the tiebreaker on the basis of their better conference record (9-3 vs 7-5). A similar analysis applies if the Jets lose.