It hasn't damaged any of my games. It'll loosen a bit with more use. The cheap 72 pin connectors for toasters are a totally different design.
As for King's Knight, first check for the green stripe on the edge of the connectors.
(Ignore the red circles, look at the pins for the green stripe.)
If it has a stripe, try inserting by gently pushing the cart up to the connector, then firmly insert left side first, then right side.