Do tones change at the end of an interrogative sentence?
It's not a question of being an interrogative sentence.  The problem is that Chinese tones in connected speech often sound different from their textbook forms.  This is something most native speakers are unaware of, and even in the specialized literature it's hard to find detailed information about it.  (The third tone rules below are well-known in the literature.)

I'm going to use Yuen Ren Chao's notation for tones: the scale goes from 1 (low) to 5 (high).  So 55 is a high level tone, 51 is a falling tone, etc.

The third tone (textbook 214 or 215) undergoes two well-known changes (search for "third tone sandhi" or "half third tone").  First, if two third tones happen in a row (你好、我想、友好), the first of the words changes to second tone: ni35 hao214, wo35 xiang214, you35 hao214.

Second, all other third tones are pronounced as 21, not 214, in connected speech: low dipping, with no rise after.  Only very rarely will you hear the full falling-rising contour -- usually for emphasis on the last word in a phrase.

Now we get into tones which are less talked about:

The first tone (textbook 55) is always level, but how high it is depends on the level of emphasis.  It will be exceptionally high if you want to stress the word: 你喜不喜欢吃..中..餐 "Do you like Chinese food" -- instead of some other option.  It will often sound quite low as the second syllable in a two-syllable word (亚洲 "Asia" ya51 zhou22) and in other contexts where it doesn't need emphasis.

The second tone (textbook 25 or 35) often comes out sounding mid-level (33) or dipping-rising (434) -- this seems to be especially common at the end of a sentence.  (I struggled with this for a long time: I would hear second tones as third tones all over the place.)

I've discussed the third tone above; the fourth tone (51) is pretty straightforward.

Now, to answer your question: 你喜不喜欢吃中餐？  I clearly hear 欢 as a first tone -- it's medium level (33) because it's "light" or "lessed stressed" but it's quite clearly a first tone.  As for 中餐, I hear it as 中 being emphasized, as if the guy had just suggested pizza, and she was saying "how about something Chinese"?  There's a natural tendency for pitch to fall over the course of the sentence, so in principle it's not surprising to hear 餐 be lower than 吃.  But this voice does sound unnatural to me, probably because it's machine-generated speech.