What does "tane" mean in this context?
Is it just stressing that you're only buying one lamp?
Not really. Normally, if you are able to physically count objects, the use of the word "tane" is optional. It is just a counter word :)
why not masanın lambsı?
Because this isn't about ownership. This is a noun compound.
It's not "the table's lamp" but "the table lamp".
Quality of sound is bad
Here i heard "bir tane masa lambası almak istiyor" and not "istiyorum". Anyone who heard istiyorum?
Yes, I did. :-) The -um is there, but the voice is trailing off, so it's a lot more quiet, almost silent. But just almost! Turn off the volume or get your ears closer to the speaker and you can hear it.
So it does not mean one other lamp
Nope :) "Bir tane" just means "one (piece/unit)"
I played this several times and I couldn't understand 'masa lambası' without finally playing it in slow mode. I guess I have to work on my listening skills.