T-tests provide info about the margin of mean difference? I have 2 unpaired datasets where the difference of the sample means is quite substantial (with the naked eye). The t-test shows that the difference is significant (p-value=0.007) and I would like to know if I can use the t-test to claim that one dataset provides significantly better results than the other or do I have to say that t-tests prove the difference is significant and use confidence intervals (or some other method) to show that one performs better than the other one?
If we go by the description of the T-test on Wikipedia: "The t-test can be used, for example, to determine if the means of two sets of data are significantly different from each other".
Based on that I believe t-tests can be used only to show if the means are different, we cannot extract info about the margin of the difference or one dataset is better than the other.

If the null hypothesis is $t=0$, then this is testing if the two means are the same or not.  But you can also test $t > a$, then this tests if the margin is larger than some number.
