This is not an easy task..
Firstly, you probably need Drag&Drop behavior here, not swipe gestures. On the video the hand grabs the letter and then drags it several rows/columns. With gestures you will only be able to slide letters one cell at a time. For example, to move the letter 3 cells up, you will need to swipe it 3 times.
So when dragging starts, you need to detect its direction (horizontal or vertical), lock this direction, and then move the entire row or column. On drop you need to snap letters to the nearest cell.
Another tricky part is wrapping the letters. As a letter disappears on one side of the board, the same letter should reappear at the other side. You need to create a copy of this letter sprite, or maybe a copy of the entire row/column.
Anyway, this is a pretty complex mechanics, not something that can be done in 20 minutes.