My notes on this game, also known as "pipelayer".
First, ties are impossible. Even if the pipes were placed randomly, or both sides tried to avoid making the last connection, exactly one of the two will do it, and at the same time create a wall permanently blocking the other.
Second, as is usual in two player games, first player gets the advantage of a move's initiative. So given ties are impossible, it's no surprise to me 1st player wins in a perfect match.
Now onto my idea of good strategy. The core idea I would present is the idea of playing to obstruct the opponent's path, rather than to complete your own.
There are two kinds of move for both sides. For purposes of this analysis, a "row" is defined according to the direction you want to go overall. For the player wishing to connect top to bottom, a row is a set of their dots running side to side. For the other player, a row runs up and down.
A forward move connects two different rows. It is required to make a certain number of forward moves to win, depending on how big the grid is. For this reason, a forward move is usually preferred.
A side move connects two dots in the same row. It is useful for bypassing a blocked path, and is often necessary. A side move will also tend to block off your opponent's ability to do the same. Side moves aren't absolutely required at all, but you'll see them nonetheless as paths get blocked.
It is interesting to note that one players forward move is oriented the same way as the other player's side move and visa versa.
Now my primary short term objective is to block my opponent's forward moves with my own. My second objective is to cut off side moves connecting his halves in the event I don't have the option to step in front of him. My third objective is to finish my path if given the chance, but this will usually occur after a great many moves and opponent's attempts to break through my roadblocks.
If I start with a forward move in the corner, and do the above, it is my contention that I will eventually win, because as I set up roadblocks, I am also building my own path. And since I have the advantage of a move's initiative, his attempts to mirror this process will fall by a move.