When the other player's Queen or Rook or Knight or Bishop moves next to my King why can't I capture them? I've only played on line computers, and they will not allow the King capture any of those pieces.
your chess king can capture the opponent's pieces as long as such a piece is not protected.
In chess always watch out if a piece is protected or not.
It is as simple as that.
Best move for Black is 1...QxR+ 2.KxQ Ne3+ (a fork) followed by 3...NxQ and Black has won a whole Rook and should win...
In this case the black Queen was not protected and the white King could capture it.
In this case the black King cannot capture the Queen because it is protected by the Knight! This means Black is checkmate because the King can't walk away to escape the check.
The Black King is in check but the King cannot capture the Bishop because it is protected by the Queen. So the King must move away from the check.