How can CFGs have epsilon rules if CSG may not have them?
The definition you state is for noncontracting grammars, which define the context-sensitive languages (modulo the issue of the empty word). In contrast, context-free grammars define the context-free languages, which are a strict subset of the context-sensitive languages.

So whoever told you that a Type 1 grammar is context-free iff it is noncontracting, used highly idiosyncratic terminology. Or perhaps they just made a mistake.

The Wikipedia article mentions a paper of Chomsky in which noncontracting grammars are called "Type 1". In an earlier paper of Chomsky, he used "Type 1" to mean context-free grammars. This might be the source of the confusion.

Finally, to answer the question in your title: noncontracting grammars only define the context-sensitive languages without $\epsilon$. Conversely, the context-free languages without $\epsilon$ are defined by context-free grammars without $\epsilon$ productions (this follows from Chomsky normal form, for example). In this sense a noncontracting grammar is a generalization of a context-free grammar, in both cases for languages without $\epsilon$. If you want to include also languages with $\epsilon$, you need to consider essentially noncontracting grammars instead; these are also allowed to contain the product $S\to\epsilon$, assuming $S$ doesn't appear in the right-hand side of a production.