Just another clarification - after adjusting my score calculations I get two identical solutions for test 4 in the IDE.
The first solution is the right answer: collected letters for maximizing player I, E, G, R, A, M, D, H (and T, C, L, F, P, S, O, N for the minimizing player) producing the score of I 29-14.
An alternative solution is: collected letters for maximizing player T, E, F, R, A, M, D, N (and I, C, G, L, S, P, O, H for the minimizing player) giving the score T 20-5.
As it can be seen both paths have the same point difference between the scores of the maximizing and the minimizing player of 15.
Maybe the puzzle statement could be adjusted to reflect this possibility.