There are two things here.
1) You are creating object of HyperLink but not adding to your UI, so that element is never going to be display, so if you have your own Popup Window(Page) then add this element there where you need to display it as link.
2) this ShowPopup(), is it from a 3rd party Javascript library, if yes then mentioned about it and probably ask in that forum.
3) on a side note, your code is not working, anyway below code will also not work :(
ClientScript.RegisterStartupScript(this.GetType(), "Popup", "ShowPopup('" + link.NavigateUrl + "');", true);
Thanks
Rushi