Old Gurgaon refers to the earlier, more established part of the city — Sectors 12 through 17 and the areas around them — built out long before the newer sectors further south existed. It has a settled, lived-in character: proper markets, older trees, and a slower pace at street level even as the roads stay busy.
Star Stayz Sector 15 sits within this part of the city, which suits residents who'd rather be somewhere with an actual neighbourhood feel than a still-under-construction sector with more cranes than shops.
The trade-off is that some of Old Gurgaon's roads and infrastructure are older too — traffic near the main markets can get heavy at peak times, same as most established parts of any Indian city. We'd rather mention that upfront than have it be a surprise.