Yes, Ukrainian "x" realy = German «ch». In Ukraine sudents studied English for many years by Russian textbooks, so most learned that English «h» = Ukrainian «х», but it is not. Also is common a transliteration of Ukrainian "г", through the English «g». It's even worse. Ukrainian "г" is similar to English «h», but in cases where the pronunciation is clear. Very similar to Ukrainian is Indian pronunciation of English. Clear «h», clear «r».
For one, г is a voiced sound. In Russian it corresponds to g from "good"— however, the Russian sound is a deviation from what the consonant was ages ago. The Ukranian sound is a fricative that can vary from a voiced English "h" to a voiced Russian "х" (or so I heard).
Х is the voiceless sound somewhat similar to "k" turned into a "sh"-like fricative sound by making it less abrupt.
I think it might be hard to hear the voicing at the word-final positon, sometimes, however, I can hear it here if I listen carefully. You see, in Ukranian the devoicing of consonants is more limited than in Russian. The end of the sentence received less energy, sure, but a speaker at least tries to pronounce the "Г" voiced.
@shady_arc, Igor, you are mostly right. Actually the situation is as follows: Г is not an English H: try to pronounce the H as in Hard, but add voice (the sound is somewhat resembling to a relieving sigh :)). What you heard (a voiced Russian Х) is not considered literary norm: it is so in Belarusian, but not in Ukrainian. In Ukrainian, Г and Х are not counterparts by voicing, they have different place of articulation. Х, on the other part, is identical to the Russian or Greek one, it's not so "harsh" as German or Gaelic ch.