That item is the 
Orchestrion, and it is actually coming as furnishing to FFXIV (Yoshi stated the basics of it are worked out, they just need time to finish off the coding for it and the like, stated in 
here and 
here). But I doubt it will allow us to play FFXI tracks. 
Although hearing tracks like 
Battle in the Dungeon and 
Recollection during that event was really nostalgic and great fun, FFXI's music was unfortunately something of a mixed bag - despite some amazing music, Mizuta also did far too many repetitive tracks that really got grating on the ears, especially battle themes, but zone music also fell into that (
Selbina and it's Irish jig was probably the worst offender, but 
Kazham was another one that made me want to stick pins in my ears by the 9000th time it looped).
Either way, a couple of nostalgia pieces are nice, but again, this is FFXIV not FFXI. Having one-off small music references like 
Terra's Theme on the Magitek Armour or FFII's 
Battle I play during certain special story battles is different to wanting the full OST replaced wholesale with FFXI's soundtrack simply for nostalgia. But then, I often play devil's advocate on this forum so I'm probably one of the few who feel this way.