How can "confession" mean praise?

Oxford Dictionary gives one meaning of confession as:

confession of faith
A statement setting out essential religious doctrine:
a Protestant confession of faith

Chambers Dictionary specifies one of the meanings of confession as

a declaration of one's religious faith or principles • a confession of faith.

This website refers to:

a "Faith Confession for Praise and Worship"

and states:

"Read the following confession several times each day to give praise and worship …"

Your question refers to "a statement by the translator that … the word 'confession' … can … be a statement of praise." and your quotation from the book actually states:

"The very title itself can be read two ways: Of confession as praise, as well as confession as acknowledgement of faults."

Note that the quotation from the book did not actually state that confession means praise — rather that confession [of faith] can be a "statement of praise". That seems to me to be supported by the stated dictionary definitions and the usage examples given above.