This year seems to correspond with the dates and days of the main year of Pale Fire's narrative (1959), other than January and February (1959 was not a Leap Year but 2020 is).
For instance the letter that Kinbote says he received from Disa "on April 6, 1959" (pg 93, Vintage version), would have arrived on a Monday, like today. (And had a fast turn-around time, being in response to a letter he had air-mailed on the Thursday before (page 257).)
(The quote in the title is from page 84.)