The KJV "of this life" does not occur in the Greek - it is simply, "of life". The three abstract nouns that are "of [this] life" which choke life include (1) anxieties/cares, (2) riches, (3) pleasures. This can be deduced from the concatenation of repeated "kai" (= and).
Thus, all three - "anxieties/cares and riches and pleasures are of this life while going are choked … " (my translation).
While the KJV version "of this life" is an interpretive translation, it is defensible on the basis that the Greek word, "bios" usually refers (but not always) to this life in contradistinction to the next life (most often "zoe"). We see this distinction in numerous places in different phrases such as this world/age vs next world/age. For example: 1 Cor 5:19, 6:4, 7:28, Luke 18:30, Luke 21:34, 2 Tim 2:4, etc.