You seem to get the meaning/importance of tempo a bit wrong - it's not about getting back to the old square, it's about losing one move during the process, thus forcing the opponent to make his turn when it puts him in worse situation (this is called Zugzwang). This is especially important in endgames, and you can see some examples in the same wiki article you are referring to.
Also note that the final square doesn't have to be the same as the starting one (e.g. Re1-e2-e3 instead of Re1-e3), although it often is (mainly in Kings' triangulation). Knight cannot do any of that, as mentioned in answer by @magd. Knight can just jump from and back to the same square, but the opponent can e.g. also do some repetitive move and you end up right where you started. Knight just cannot take the route to its' destination which will lose exactly one tempo (or any other odd number).
But all other pieces (even pawns if they are at their starting square) can take an extra move while going to the destination, which in many situations enables you to force the opponent to make a move when it's a bad time for him. Triangulation is a classic example of this tactic.
Generally speaking, losing tempo or just getting back to the previous square is usually bad in openings or even middlegame, although that depends on the situation. But in the endgame, deliberate loss of tempo is often maneuver which wins you the game (of course, if situation requires so).
An example from wiki:
[fen "8/1p1k4/1P6/2PK4/8/8/8/8 w - - 0 1"]
If black would be on the move in this position, it would be clear victory for white, as after black King moves away, white can proceed either with his King or his Pawn (depending on the move). But white is on the move, so he must think of a way how to make it work. The answer is, lose a tempo with triangulation:
[fen "8/1p1k4/1P6/2PK4/8/8/8/8 w - - 0 1"]
1. Ke5 Kc6 2. Kd4 Kd7 3. Kd5
And now black is on the move, which enables white to break through.
You are right in saying that loss of tempo is used "only" to put opponent in zugzwang, but the importance of this is greater than it might seem at first. For example, every classic mate endgame uses loss of tempo and zugzwang to get the opponent's King to the edge of the board and to mate him. You often use zugzwang without even realising that you used it. Look at the mate with Rook:
[fen "1k6/7R/2K5/8/8/8/8/8 w - - 0 1"]
1. Rg7 Ka8 2. Kb6 Kb8 3. Rg8#
You aim to get your King to b6 when black King is on b8, so you can mate with Rook on 8th row. But you can't do that right away, as after 1. Kb6, black would get away with Kc8, and 1. Rh8+ would enable black to get away with Ka7. So in the process of getting to 8th row with your Rook, you deliberately lose a tempo with 1. Rg7 in order to win the game.
In contrast, to address your original question, Knight is not able to do that:
[fen "8/8/8/8/8/7p/5K2/5N1k w - - 0 1"]
1. Ng3+ Kh2 2. Nf1+ Kh1
If white could just get to the starting position with black on the move, it would be a quick victory (1... h2 2. Ng3#), but Knight can't lose a tempo, so it's impossible, which is why this position with white to move is a draw.
