I think that's a proprietary in-house emulator known as POPS. The fact that Sony already had an in-house PlayStation emulator for the ARM-based Vita makes their decision to use something else for the PS Classic a bit strange.
I imagine some third party approached Sony with a "we'll do the work, take the risk, etc. You just give your blessing, tell us who do we need to contact for final approval to make sure the brand is being well represented, and where to send the royalty checks" kind of deal.