I hope that I can help you and I giured out what your problem is correctly. I made a quick demo in paint (it doesn't look great, but it's the best I can do.)
I think that what might be tripping you up is the same thing that tripped me up: the first row of triangles. It's a complete anomaly because you only do it once at the start to get the ball rolling. After that, you will alternate between what I have labeled Row 2, which is made up (from left to right) of a triangle that points to the right, two squares that lean to the left and a triangle that points to the left. In order to get this row started, you need to pick up the stiches from the rightmost edge of your rightmost triangle from the fast on section (see the top illustration in my paint diagram).
The other section you will repeat is what I have labelled Row 3 (the blue). It is just three squares that lean to the right. In order to start that row, ignore the diagram I made. I messed it up--sorry! What you should do instead is pick up the stiches from the left triangle of Row 2.
Once you have finished Row 3, you will repeat Row 2 again, picking up from the right edge of the rightmost square of Row 3. Then do Row 3 again, etc, until the scarf is as long as you want to be, then follow the instructions on Yarnpath to cast off.
So, to answer your question, I guess you are supposed to get rid of the stitches from the first triangle.
If this doesn't answer your question, let me know and I'll try to help you out further. Good luck!