I am aware that in most chess games the king is the one to be checkmated. Yet when playing many online chess games I have found the queen is the the one being checkmated. Is this simply another variation of chess?
The short answer: because it is the most valuable piece after the king.
The long answer: For a piece to be trapped two things must happen: you need to threaten to capture it, and you need to make this in a way it can't escape or be protected without loss of material or a positional drawback suck as mate.
For a piece to be protected effectively, the piece attacking it must be more valuable than the piece being attacked, so any piece can attack the queen and if there is a trade the attacker will gain a material advantage. So other pieces can be protected in more ways than the queen.
For a piece to be able to escape, it must be able to move, and it needs a safe square. The queen is the most mobile piece, but moving in straight lines, it can be easily blocked by another piece, and any piece can do this, since a trade would mean material loss for the defending side. So the queen can be blocked in more ways than most pieces. For a square to be safe for the queen, it needs to be free from attacks (except from the opposing queen), again, since any trades that happen after the queen moves to that square will result in material loss. Other pieces can move to squares attacked by stronger pieces, if the defender has another piece protecting that square. So the queen has less safe squares available than most pieces.
That sums it up, but there are MANY exceptions when you take into account the actual position, since a square can be safe if moving to that square uncovers a discovered attack with a mate threat, or many other situations.