The authors did actually say what δ means in words here: "For storing n elements and ensuring correctness with probability at least 1−δ, existing constructions

The authors did actually say what δ means in words here: "For storing n elements and ensuring correctness with probability at least 1−δ, existing constructions require <blah>. With a failure probability of at most δ, our structure requires <blah>". There's some fluency with the language required to understand what a free variable is, and that a sentence structure like "with probability at most δ, our thing does X" is introducing δ as a free variable. There's also some background "cultural" knowledge required to quickly parse out the fact that probabilities are between 0 and 1, so correctness probability 1-δ is the same as failure probability δ. Maybe they could've been intentional about avoiding that, but it's also normal (and even considered good style!) in natural language to phrase the same idea slightly differently from one sentence to another. It's also pretty clear what Ω means in context even if not explicitly spelled out. They say an existing thing needs Ω(...) space and fully random hashes, and their thing needs O(...) space and O(...)-wise independent hash functions. Clearly they're talking about bounds on things, and Ω and O have standard uses in that context.