Economic rent is hard to wrap your head around; I defer to the Wiki:
In classical economics, economic rent is any payment made (including imputed value) or benefit received for non-produced inputs such as location (land) and for assets formed by creating official privilege over natural opportunities (e.g., patents)
In neoclassical economics, economic rent also includes income gained by beneficiaries of other contrived exclusivity...
In layman's terms I think it could be described as income for having/being rather than income for making/doing.
What you described is nearly precisely the definition of market power. Economic rent is, from what I've read (IANAE), a special case of market power that applies to factors of production (particularly land).
Most theories of profit assume that an investor gets money approximately proportionate to the risk they take in investing as a well as to the opportunity cost of just sitting on their money.