The 3-letter path: JOB
Trace JOB straight across three cells: 1 at row 1, column 5; 2 at row 1, column 4; 3 at row 1, column 3. The letters appear as J → O → B, with two consecutive moves to the left and no turn.
This route occupies one straight segment spanning three columns within one row. All three cells touch the board edge, including one corner visit. Its starting cell has one open orthogonal neighbor, while its ending cell has three. Assigning this path covers 3 of the 18 open cells and leaves 15 for the other three words.
For a quick route check, count two movements and make sure both go left. Any turn would contradict the one-segment geometry, while any additional step would exceed the required length of three. This compact horizontal trace also explains why its row span is one even though its column span is three.