its popping out slightly, the push pin wont stay attached to the motherboardWhat do you mean popping out a little more? Its got push lock pins and should not move up down left or right, Unless one snapped?
That block is your South bridge, look at the following image.
Of course different factors change with newer architectures, But the base functionality of the Southbridge has largely stayed the same as its a solid method.
So it could cause issue if the heatsink is slightly detached.