A question about the word 'blood' meaning 'a close relative'?

"The only blood left" refers to the remaining members of a family.

The same use of blood occurs in bloodline = "all the members of a family group of people or animals over a period of time, especially when considering their shared family characteristics".

Cambridge Dictionary online

It relates to genetic connection rather than to marriage, so a long bloodline is a line of genetic connection going back through parents, grandparents, great grandparents ... Having "royal blood" is a genetic connection to royalty.

Apparently an AmE expression:

blood relative (US)

someone who has the same parents or ancestors as another person

• Your sister is your blood relative, but your brother-in-law is not.

(Merriam-Webster)

This connotation of blood is actually quite old:

Meanings "person of one's family, race, kindred; offspring, one who inherits the blood of another" are late 14c.

(Etymonline)