Hmm..... Your niece and nephew are adopted? If not, they're surely your blood relatives.
You're right. I thought a "Blood Relative" had to be someone from the same parents. Looks like a niece & nephew are "2nd Degree Blood Relatives" (if the info on this site is correct). Never too old to learn something, eh?
According to the National Genetics and Genomics Education Centre, blood relatives are classified as first-, second- and third-degree relatives. First-degree blood relatives include parents, siblings and children. First-degree relatives share approximately half of their genes with one another.
Second-degree blood relatives are uncles, aunts, nephews, grandchildren, grandparents and half-siblings. Second-degree blood relatives share approximately 25 percent of their genes with one another. Moreover, in the United States, first cousins, first cousins once removed and first cousins twice removed are considered second-degree blood relatives.
Third-degree blood relatives are great-grandparents or great-grandchildren. Approximately one-eighth of genetic material is shared between third-degree blood relatives. In the United States, second cousins are considered third-degree blood relatives.