The writer is selling his own book.
look and compare
'they' and 'their' are very often used these days as non-gender-specific singular pronouns. I would say this is now very much the preferred form. A few people still write 'he' and 'him' when the gender is unknown, but this is widely considered to be undesirable. More recently still, it has become quite common to use 'they' and 'their' as singular pronouns even when the gender is known.