The hand-wavey text in the top-left explains that "Banks and governments in these five shaky economies owe each other many billions of euros."
So while it does look like "Greece owes Ireland $8.5bn" is at least partially cancelled out by "Ireland owes Greece $0.8bn", I would expect that these statements roughly translate to "The Greek government owes various Irish banks $8.5bn" and "The Irish government owes various Greek banks $0.8bn", which unfortunately don't cancel each other out.
So while it does look like "Greece owes Ireland $8.5bn" is at least partially cancelled out by "Ireland owes Greece $0.8bn", I would expect that these statements roughly translate to "The Greek government owes various Irish banks $8.5bn" and "The Irish government owes various Greek banks $0.8bn", which unfortunately don't cancel each other out.