Hybrid Chat uses Routing Engine for a human agent selection for a give request. It does attributes based resource selection based on multiple steps defined for a particular queue. See MRE User Guide for details. For an architectural overview, see the architecture and communication flow.
It works both with Cisco UCCE and UCCX for media blending and uses Cisco contact center Agents. However, you'll need to define Attributes (skills) and Queues in the Routing Engine. See Cisco Contact Center Integration for details. It routes all non-voice media requests to the blended-agents.
For Routing Engine APIs, see MRE 3.x APIs.