The Chiefs held their rookie minicamp over the weekend. There were seven drafted rookies, 11 undrafted free agents, seven "first-year" players (as defined by the NFL) as well as a handful of tryout players.
Williams was one of the "first-year" players as defined by the NFL (he didn't have an accrued season). He was signed to the Chiefs practice squad last season and eventually signed a future/reserves contract with the Chiefs following the season.
The interesting note about him is that he missed time in the rookie minicamp due to injury. He was in No Man's Zone working on the exercise bike during practice.
The other player, T.C. Drake, was a tight end who was signed as an undrafted free agent.
This leaves the Chiefs at 76 players under contract. They can have, at a maximum this time of year, 80 players under contract. Keep in mind, however, that the seven drafted rookies are not under contract yet.