Should node.js replace Web API? No.
What's the use of having both Web API and node.js? They're apples and oranges. While it's possible to use node for things you could with Web API, node can be used for more than fulfilling HTTP requests.
Perhaps node isn't a good first choice for ORM data access to SQL data stores, but it's quite adept at ORM data access to various NoSQL data stores like MongoDB and Redis.