Why do you think that children's participation rights matter?
Children's participation rights matter because they are the ones directly affected. We must encourage them to be active participants in things (laws, programs, human rights instruments) in order to reach the most optimal outcome for everyone. I liked when Landon Pearson said somehting along the lines of "children have to not only be listened to, but heard". Sure, we can ask a child's opinion on an issue, but unless we actually take them seriously and give them credit where it is due, we are not advancing.
Encouraging children to participate at a young age also encourages them to pursue their rights. It also gives them the confidence to defend themselves against violations and empower them to share their knowledge with others. If we honour their participation rights, we raise a whole new generation of informed, empowered individuals to help re-shape the world.
How does the inclusion of children's participation in the UNCRC implicate States Parties that have ratified the treaty?
It means that they have a duty to children, to fulfill. It means they owe it to the children of their area to make sure they are listened to and included in decision-making processes. It puts the onus on them to do what is best for the children.
What do children's participation rights have to do with citizenship and democratic processes that are inclusive and empowering?
If children are viewed as willing and able members of their society, it effects their rights to vote. If they are seen as equals, it should mean they, too, have a right to the workings of democracy. However, as Lansdown mentions, it must be based on their maturity level. They must be fully able to understand their choices and be able to make conscious decisions about voting.
That being said... We do allow adults (18+), who do not act as maturely as we hope they do, the right to vote. The social construct of "age and ability" is one that is tricky as age does not always equal maturity.