Hi james1.

HTTP 2.0 ( https://tools.ietf.org/html/rfc7540 ) Server Push is not a replacement for WebSocket ( https://tools.ietf.org/html/rfc6455 ) . The Server Push potentially allows the server to avoid this round trip of delay by “pushing” the responses it thinks the client will need into its cache, so it is used behind the scene to improve resource loading by the client from the browser.

WebSocket for the other hand provides a full-duplex communication channels over a single TCP connection. For example allows for the creation of an API which is able to consume and push message with an UNIQUE full-duplex connection. The Graphene API which power up the Bitshares blockhain (and this steemit.com) uses the advantage of a full-duplex API interface http://docs.bitshares.eu/api/index.html#interfacing-with-graphene

Basically it is not a replacement, they complement each other.