Gra półsłówek is Polish for
Spoonerism.The phrase "Gra półsłówek" is a spoonerism itself, as when you exchange the initial letters, you get "sra półgłówek" which means: "a dumbass is having a shit".
I'll try to translate the least obscene of the examples on the website you linked:
chodzenie w płaszczach - wearing coats=> płodzenie w chaszczach: begetting in bushes
elita wieprzy na piecu: the elite of hogs on a stove => elita pieprzy na wiecu: the elite is talking bullshit on a rally
Jacek na wózku: Jack on a rally => Wacek na Józku: Wacek (a male name) on Joseph
Kędy z miłą? : Which way to go with my beloved? => mendy z kiłą: crab lice with syphilis
kupy w trawie: pooh in the grass => trupy w kawie: corpses in the coffee
pradziadek przy saniach: great grandfather by the sleigh => sra dziadek przy paniach : grandfather is shitting in ladies' presence
The other examples on the list are much more 'indecent'. And more funny...