Your example is not wrong, but I would not use it in that setting.
In the Cambridge dictionary example, the important point is that there are two sets, countries and capitals, each of those sets has the same number, and there is a one to one correspondence between the sets. In other words, there is exactly one capital for each country, and one country for each capital. It's not possible for London to be the capital of England, Germany and Australia all at the same time.
But in your example, that one to one correspondence probably doesn't exist. Suppose you have 10 people and 10 duties. What will you do if 6 people in the group choose "dishwasher" and no one chooses "gardener"?
What you want to do is to find for each person a duty they are happy to do. Suppose you give each person a list of the duties and ask them to tick or select the duties that they are willing to do or consider themselves suited to. Then you might collect the lists, review them, and based on their replies you might choose a specific duty for each person.
If that process occurred, there would be a matching in the sense you have given. But the matching would happen not when the group members chose their preferred duties. It would happen afterwards, when you made the allocation of one person to each duty.