Hello Ilian,
I did a quick experiment by changing the rank offset of a list of scores . The original ES was -0.26, but you can see in the plot below that adding or subtracting from all of the values had pretty different results. Most GSEA lists vary from a negative score to positive scores, where the median value probably is close to 0. In the normal list, when these median values are encountered, they will add very little to the running sum since their absolute value is small. The values on either end of the rank list will have larger absolute values, so they will have a larger effect on the score. When you shift the score up by add a positive constant value, the negative scores of the ranked list will have less of an effect on the running sum, since the absolute value of the negative ranks is now decreased. If you add too large a value, this would make the ES to change sign, which is what I observed in my quick test. This is a possible explanation for why you observed different results. I would guess the extent of this effect would vary on the rank distribution of your list and the value of the offset. Let me know if this is helpful. There may be more effects, such as the random permutations that will change your results, but I believe this is the underlying cause for the difference in results.
Best,
John