Translation:Who wants to go to the disco with me?
That might be because discotheques - and in fact, disco music - didn't exist at all until about 1976 or 1977. :-) Technically, the word "discotheque" itself existed much earlier, but it didn't come to mean 'a club where one goes to dance to disco/popular music' until around that time.
If the noun denotes some part of landscape, an object you climb, a roof or other open space, or an event, then the preposition на is required. Examples: на пляж, на берег, на гору, на этаж, на крышу, на дерево, на стадион, на концерт, на спекталь, на балет, на представление, на танцы, на дискотеку, на выставку. (Mind the difference: залезть на дерево (climb a tree), сидеть на дереве (be sitting in a tree)). If, however, we are talking about a building, a room or a cave, a park, a garden or a forest, then we need to use в. Examples: в театр, в музей, в школу, в кино (here кино=кинотеатр), в комнату, в пещеру, в парк, в сад, в лес. While talking about direction of movement, we can say both на реку/озеро (to the river/lake) and в реку/озеро (into the river/lake), на море (to the seaside) and в море (to the sea). We say я вышел на дорогу (I came to the middle of the road) and я взял еды с собой в дорогу (I took some food with me when I set off for the journey). We also say, отправиться в путь (to set off) and пора в дорогу (time to set off).
I can’t listen to the recording and check what the speaker is actually saying, but, given that he is a native, it seems to me that you must have misjudged the place of the stress in the word дискотека. The thing is that, in any Russian word with more than 2 syllables, two vowels are pronounced clearly as full vowels — the one that takes the stress and the one in the preceding syllable, although the latter is a little bit weaker than the stressed one. The letter о in the syllable that precedes the stressed one is always pronounced as а (i.e. as u in up). The vowels in all syllables except the said two ones are reduced (weakened) to a shwa (in the case of а, о and sometimes е) or a very short and vague variety of i (in the case of и, е and я) or oo (in the case of у and ю) or a blend of shwa and short i (in the case of ы). So when you hear the full а for о in дискотека, you think that the stress falls on the second syllable, but actually it is the 3rd syllable that is stressed. The illusion of the stress shift comes from the fact that an English word cannot have two full-vowel open syllables in a row, whereas in Russian this is normal. By the way, that is the reason why most Russians struggle to pronounce the indefinite article ‘a’ correctly and say ‘ubbook’ or ‘eh-book’ instead of ‘a book’. Also the overwhelming majority of Russians are misled into thinking that there is a difference in pronunciation between ‘a clock’ and ‘o’clock’.