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). The beginning of the list of three nouns is (as expected) initiated using "hupo" (= by). So Luke 8:14 reads (literally):
"these are the ones having heard, and by anxieties/cares and riches and pleasures of life while going are choked and do not bring fruit to maturity" (my translation). Or from the ESV 9or(or similar) "they are those who hear, but as they go on their way they are choked by the cares and riches and pleasures of life, and their fruit does not mature." The NASB has, "these are the ones who have heard, and as they go on their way they are choked with worries and riches and pleasures of this life, and bring no fruit to maturity."
The force of this sentence is, "these are the ones [despite] having heard … are choked …" That is they allow the things of this world to distract them from eternal realities in spite of the fact that they have heard the gospel.
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 15:19, 6:4, 7:28, Luke 18:30, Luke 21:34, 2 Tim 2:4, etc.