EDIT two years later.
Sorry, all my image links turned bad. I cannot post an image here directly, as far as I can tell.
Instead, I refer you to the thread
https://www.boardgamegeek.com/thread/1665337/why-you-need-be-able-link-between-pegs-yours-alreaon the Boardgamegeek Twixt forum. There are six images there. I refer to them here as images 1 through 6. So, if you want to to discuss this topic, you could refer to them in the same way. Or, you could post a response in that thread instead. I will try to respond more quickly from now on.
Here is a variation from a game I recently played.
[image 1]
It is purple's turn. On this server, I could remove the H5-J6 link and then play i5 linking to H7:
[image 2]
But if I did that, yellow would win immediately with J4:
[image 3]
Under standard rules, the only way for purple to win is to place a peg at i5 and do *not* remove the H5-J6 link, do *not* add a link from H7 to i5 *on this move*.
[image 4]
yellow cannot prevent purple from adding the H7-i5 link later. Play might continue with yellow playing at K4 to prevent purple's double link from i5 to J6,
[image 5]
And now purple wins with -i5'/H'6K6 (using Alan Hensel's notation at
http://www.ibiblio.org/twixtpuzzles/[image 6]
But such a move is not possible on the TwixtLive server, because there is no way to add a link between two pegs already on the board.
Of course, this pales in comparison to the importance of adding the swap rule, but I thought I would mention it anyway.