It is certainly ambiguous, which is of course why you are asking for the meaning in context.
First of all, I don't agree that the Macmillan Dictionary is doing a complete job defining "commitment" with those definitions. You want to consider its relationship to the verb "commit" more thoroughly. Nevertheless, I would say it most likely is meant as "a strong belief in something". However, it's difficult to separate their "strong belief" that working with local residents is good from their "enthusiasm" for working for working with local residents. They go together and the speaker probably intends both meanings.
It does not make sense that they attribute their success to a "promise" they made. They might attribute their success to the actions they took to fulfill that promise, but it is unlikely that the promise itself was contributory. In other situations, though, the promise itself could be what is being referred to. For example "My son got straight A's in school this year due to my commitment to buy him a car if he made the honor roll."
It does not make sense that it was a "duty/responsibility" for them to work with local residents, because the general sense of the sentence is about how the choices the Conservancy made led to the success of the project. If they were acting out of duty, then you would be making another point which you would want to make by phrasing things differently.
"Use of money" does not fit "to working with local residents." Use of money would be more like "... and our commitment of $300,000 to habitat restoration."