Here is a word game; I hope that you enjoy it.
To clarify a bit on the part of "Every letter belongs to a group of four letters, and this bond must be maintained", here's a picture showing a valid configuration (though it is not a valid solution, since the rows and columns do not yield any words):
One line shaped segment, one square segment and two L-shaped segments are used, of which one is reflected. Though no rotations are present in this example, these are also allowed (e.g. it would be valid to rotate this picture 90 degrees, though this would still not give a valid solution). Also note, that while I've adhered somewhat to the ordering as given in the problem statement, the letters can be arranged in any order, i.e. the first line might just as well be slge.