The answer is twofold. First of all, for several decades there has been a shift from using 'g' to using 'x', so that for example the English name Heath is Xit, not Git. But established transliterations are retained, like the ones you mention. Second, from this we deduce that the use of 'g' must be some sort of tradition unrelated to the way Russian is pronounced now. Third, we know that large parts of (Southern) Russian speak dialects where 'g' is replaced by 'h' or some similar sound (e.g., what phoneticians write with the Greek letter gamma). Fourth, putting all this together we may hypothesize that the tradition that gave us 'Gitler'
and so on goes back to a time when that S. Russian pronunciation was more widespread, so that when they wrote 'g' they actually pronounced 'h' or the like. Fifth, Ione would have to see if there is other evidence for this hypothesis, and/of if some other hypothesis can explain the facts. But in general traditions like this clearly exist in various languages, that is, traditional ways of rendering foreign sounds that have no contemporary justification. F.ex., it is easy to show that American English speakers who have never heard a Parisian 'r' and have no idea what it is they are hearing (I mean without being TOLD it is an 'r') actually hear it as an 'h' and repeat 'h'!! But we have a tradition, in this case supported by the power of the written word, that we should use our 'r' when rendering French, and so we do.