I can't see your pretty histogram of a q-q plot. It is likely approximately normal but your huge sample over powers the test saying there is a slight departure. The normality of residuals is what is important, but with that big of a sample and a reasonable histogram you are probably fine with a ttest. There is also something called a permutation test that you can use in lieu of ttest.
From the part of the histogram that I can see ... the histogram is not symmetrical
Hence I assume Latriuz should the Mann-Whitney U. Anyway I assume you don't lose much as the Mann-Whitney U Test has 95% efficiency compared to t-test.