Is my amplifier correct?
That is not good.


You have no current limiting resistor to the base of the transistor.  This can cause the transistor to fail (burn out.)
You have DC going through the speaker at all times. This can damage the speaker.
You have nothing to limit the current through the speaker and transistor.  If the transistor fails short, you have all the current the 3.3V output of the Pi can provide going through the speaker.  This could cause your Pi to crash.  If the speaker lasts long enough before burning out, it could damage the Pi.


As for the ground, that's through the second wire of the earphone jack.

There are simple, 1 transistor amplifier designs on the internet.  They work well enough.

There are many more circuits using dedicated amplifier chips that are as easy to build as a single transistor amplifier, but which will work much better.