Looks similar to sequelize query API, direct link: http://docs.sequelizejs.com/en/latest/docs/querying/

This kind of things looks better in homoiconic languages.

I'm wondering how that approach compares to rho/rewriting calculus.

Looks cool, I haven't heard of it. However I don't think I could use their querying language separately from the ORM.

Our use case for Queryl is to filter array of objects based on different criteria, but I guess an extra benefit is that the query language is completely decoupled from its usage, so anyone can use it in their own projects for different needs.