Initially, only C7 is the S^3 device that supports swype application due to some issues of it on N8. Now dailymobile.se posted an updated regarding swype's availability for n8.
Open this link on your n8's web application http://store.ovi.com/content/58438
or just search swype on ovi store
I downloaded it right from the ovi store. After installation you will see "Installation error". Just ignore it. Maybe because swype is not really a standalone application but rather an add in on the virtual keyboard for n8. Don't forget to restart the phone after installation.