The second image is a handwritten copy of the first image, and shows the year as 1764.
The first image shows why someone has incorrectly transcribed this as 1765. Starting with the entry 2 above the one for Daniel and Thankful, the month and day are recorded in addition to the year. When looking several entries down, it is clear that the year is first, followed by the month and day. However, the first entry with a month and day doesn't have the year above it, and for the next 5 entries, the month and day are written opposite the names while the year is written above and easily interpreted as being for the previous record (it is about halfway between). The year for the marriage of Daniel and Thankful is 1764, and the year of the next marriage is 1765.
