The incident, which occurred near The Camden Arms in La Belle Alliance Square, was captured on CCTV that was later released by the RSPCA.
In the 17 second clip, the animal's attacker seemingly dances down the road with the black cat at arm's length.
The animal is then seen colliding with the arm of another man. The cat's head nearly hit parked cars and a brick wall as it was violently swung around.
He escaped injury but Mrs Buchanan, a 43-year-old IT teacher, told the court he was left traumatised by his ordeal.
Witnesses testified of seeing a group of youths swinging around what looked like a cardigan before realising it was in fact a pet cat.
RSPCA prosecutor Rowan Jenkins said Lynne Jarvis, one of Mrs Buchanan's neighbours, heard "horrible laughter" and went out to remonstrate with the group.
Miss Jarvis, 62, said other people with the man swinging the cat "were jeering and loving every minute of it", he said.
The man put the cat down after Miss Jarvis swore at him, the prosecutor said.
Miss Buchanan was told about the attack by her neighbour when she returned home from work later that day. Mowgli came home at 9pm and seemed withdrawn but physically fine.
Since the incident the cat was too frightened to go outside and his behaviour dramatically changed.
Mr Richards gave the RSPCA permission to search his home but nothing was found to link him to the attack, magistrates were told.
Dismissing the case Gillian Monk, chair of the bench, admitted the CCTV footage of the attack was of "such poor quality that it is hard to identify any distinguishing features". Having considered the case she added there was "no case to answer".
"Cruelty of any description is abhorrent to civilised society and we are saddened and sickened by the way that cat was tortured that morning," she said.
"No forensic evidence was found at the defendant's home or on his computer and finally, whether or not Mr Richards was present at that incident that morning I have not seen or heard evidence that can securely place his hands on that cat."
Outside court Mrs Buchanan said: "I just feel so very disappointed, very upset and very angry.
"The past eight months have been very hard. There has been no justice done.
"I just want to say thank you to everyone who supported me during this, sending me presents and cards. I am just sad."
Mr Richards, who was unemployed at the time of the incident, had denied one count of causing unnecessary suffering to a cat. Wearing a dark suit, white shirt and tie, he was was visibly relieved at the magistrates' decision.
He said outside court: "I am relieved, it has been an awful time, especially as I only lost my mum two years ago."
The RSPCA said it was "very disappointed" with the decision but added that inspectors would not continue searching for any other suspects.