I know that dolphins invent quite complex games and partake in recreational drug use, as well as blow bubbles to amuse themselves. New Caledonean crows create tools for foraging and the complexity of those tools improves over generations and spreads like human culture. Orang-utans build umbrella like objects to keep dry, and Chimpanzees have been taught to do all kinds of things and pass that knowledge on.
I haven't seen any examples of the combination of inventive recreational activities with practical tool creation to create recreational objects, however.
The closest to a tool made by a animal with the only purpose of playing that has come to my mind are sticks used by young chimps "girls" to play with them as dolls.
Young females of the Kanyawara chimpanzee community in Kibale National Park,, use sticks as rudimentary dolls and care for them like the group's mother chimps tend to their real offspring. The behavior, which was very rarely observed in males, has been witnessed more than a hundred times over 14 years of study.
"The stick serves no immediate function, they just carry it—sometimes for a few minutes, other times for hours," study leader , a biological anthropologist at Harvard University, said via email.
The article after telling about this behaviour on natire versus nurture and maternal instinct that, well, it is not exactly of my taste. But they have documented the use of these dolls, by females -what is an added point- and thus have gained my sympathy.