I promptly received emails from two readers explaining to me that there are 77 players listed on the roster at the Chiefs website.
Correct. There are 77 players listed, However, in the context of NFL roster cuts there are 76 players.
The Chiefs do own the rights to 77 players but only 76 are under contract.
Jarrad Page still is unsigned. Therefore, he does not count against the Chiefs roster when they're going through these roster cuts.
So, until/if he signs, he is not a factor. The only way he can force the Chiefs hand to do something is to come in and sign his tender and then he would be taking up a valuable roster spot.
If he doesn't sign by week ten he'll lose a lose a year of credit towards free agency but I don't think many expect the next CBA to increase from four to five years the threshold for free agency so Page, who is entering his fifth year, may not be affected by that (The threshold is six this year, per no salary cap season rules, which is why Page is a restricted free agent in the first place).