IANAL, but this definition leaves a bit to be desired. I thought the term "civil law" is almost universally synonymous with the law other than the criminal, constitutional/non-law-of-nations law even in non Common Law countries. Specifically, it is used for law with roots in the Code civil (as opposed to Code pénal etc.) in those parts of Europe having Napoleonic law traditions, with connotations of Enlightenment and positive right theories.
1. The legal system [1], based on Roman law, that is common in former French colonies across the world (e.g. Quebec, Louisiana, France).
2. In common law legal systems, the branch of the law that deal with non-criminal matters [2].
[1]: https://en.wikipedia.org/wiki/Civil_law_(legal_system) [2]: https://en.wikipedia.org/wiki/Civil_law_(common_law)