The definition is sourced from here[0], and says "Each check-in is then verified by an automated build, allowing teams to detect problems early.". It's not a hard rule to "not run on every dev branch".
"continuous integration" is often just "npm ci && npm run build", and sometimes "npm run test" (or similar for your language). For products that don't make any remote API calls (or when they use a faker service), most of this is done on the same machine and costs very little to do on every commit, making it easier to precisely define which commit broke something.
Rather than being pedantic about the definition, maybe you could share your experiences with why that’s superior to validating each branch? Being dogmatic about a definition rather than experimenting with works best in production at your business seems illogical.
https://en.wikipedia.org/wiki/Continuous_integration