I mean the wikipedia literally states:

> CPE generally refers to devices such as telephones, routers, network switches, residential gateways (RG), set-top boxes, fixed mobile convergence products, home networking adapters and Internet access gateways that enable consumers to access providers' communication services

From my understanding any type of device that is used to extend or facilitate provider services is a CPE. So a router just acting as an extender would still be a cpe, as would a modem, as would anything that is on the customer side and facilitates provider services. Only situation a router wouldn't be a cpe is if it was just for a local lan network.