no more washing up for me

[frindle2]

Hello. Would you please tell me what the underlined sentence means in the context below?
Does "washing up" mean dish washing here? I just don't feel a connection between washing up and a rich man.
Thank you.

From the picture book, <Return to Moominvalley> by Tove Jansson---------------------

(There was a trial to find out to whom a big ruby belongs. Sniff is greedy and a bit of a coward in the book.)

“Jurors, have you reached your final decision? To whom does the Ruby belong?”
The Woodies turned and pointed – to the Groke! Sniff grabbed the ruby straight away.

Sniff grabbed the ruby straight away.“Ha! I’m rich, rich, rich! No more washing up for me!” shouted Sniff, dancing about.
The Groke slid silently towards him. She held out her paws for the ruby.

 

[Rover_KE]

Does "washing up" mean dish washing here?

Yes – in British English.

It has a different meaning in American English.

 

[frindle2]

Thank you. What does it mean in American English?

 

[Rover_KE]

washing themselves

 

[Tdol]

I just don't feel a connection between washing up and a rich man.

Actually, a person who has just claimed to have come into money. Sniff will probably be back washing the dishes while the Groke enjoys her wealth.