I had a Paph. liemianum that grew a small leaf where each bract should've been. It was just a one-time fluke.
I also had a Cattleya bowringiana 'Splendens' FCC/AOS that grew a keiki with roots, at the base of an old flower spike, nestled inbetween the two leaves at the top of a very tall, mature pseudobulb. So, strange and unexpected stuff can and does happen now and then.
Whether or not your plant grew some exagerated bracts, or that's really a keiki, depends on if there's any rhizome tissue where those two leaves meet at the flower stem. It's possible that it could be a keiki; but, it's more likely just some overenthusiastic bracts and there will be no root buds or rhizome tissue and therefore, no live eyes for it to continue growing.
However, sequential blooming Phrags can be meristemed from the growing flower stem tip and of course, besseae is a sequential blooming Phrag. Oak Hill Gardens did this with Phrag. Sedenii 'Blush'. So, perhaps the meristematic tissue at the tip of the developing spike actually did differentiate into the right kind of tissues to actually form a complete "clone", or keiki, which can be removed and coaxed to grow roots. It'll never grow roots if you leave it up in the air like that. So, see if you can rig up something to allow roots, if they are possible, to grow.
