How to play FM Radio app without earphone?

No. You need an earphone, or anything that can plug into the earphone jack, with a trailing cable.

This is to provide the phone with an antenna. Because space inside the phone is highly limited, it's usually insensible to have a built-in FM antenna.

Usually, you can still instruct the phone (or at least the FM app) to output audio to its speaker, even when earphone is plugged in, as it's primary function is to serve as antennae.