Translation:If he was thirsty, he would drink even water.
I disagree. "If I were" is correct only if you are stipulating a condition contrary to fact. For example, "If I were king" -- but I'm not.
In the sentence here, however, the "if" is not contrary to fact but is rather the equivalent of "when/whenever"-- When he was thirsty, he would drink even water. In this case, "If I was thirsty" is correct, but not "If I were thirsty".
Nowadays many English speakers ignore the subjunctive and say "Ïf I was" all the time and never "If I were". There is therefore a temptation to "hypercorrect" and change every "If I was" to an "If I were". But there are some times when "If I was", and only "If I was", is in fact correct.
You are right regarding the grammar, but the improbable condition applies here. You can see that from the use of "he would," which describes something other than reality. Thus, "If he were thirsty" is the right expression in this case.
You're wrong because the first conditional (more probable) would be "If I am thirsty, I drink", but that does not correspond to this sentence. "By" translates to "would" and "kdyby" translates to "if he were", which are both second conditional forms (less probable). Therefore, the correct translation is "If he were thirsty, he would drink" (second conditional).