Hello Justin
Frame relay is a layer two technology and as a result, DLCIs do not traverse a router. In this example, the Frame Relay Switch is actually physically a router, a layer three device, but its functionality in this case is a layer two device. This can be seen clearly by the encapsulation of type “frame relay” that is specified in the config. Specifically it is switching between one DLCI to another, something that the ISP would do for the customer.
The only layer three devices here are the two customer devices. Now the DLCIs and their scope actually ends at the routers themselves, in a similar way to how MAC addresses have a scope within the specific network segment in which they reside.
So to specifically answer your question, this is a layer two connection between the customer and the ISP frame relay switch. Indeed it is a layer two connection all the way to the remote site as well. There is no layer three functionality that is intervening between R1 and R2. The switchover from DLCI 102 to 201 is an exclusively layer two operation.
I hope this has been helpful!
Laz