An easy and quick (and probably unsatisfactory answer) is that reading was considered one of the regular free-time activities that a person, especially of the middle or upper class, would regularly engage in.

As you suggest, it's not a perfect analogy, but comparing it to television watching is helpful. In fact, people often read together, sharing interesting passages of whatever book they were reading. To quote Kate Flint, "Victorians might discuss their reading with family or friends, join a reading circle based on the ideal of self-improvement, read literature according to syllabi prescribed by schools or, by the end of the century, by universities." What one read mattered a great deal: it was a sign that someone was serious and contemplative to spend an evening or morning reading the Bible, while the more scientifically-minded could read one of a vast array of scientific journals or books, and reading popular novels was, by this time, widely accepted.

I should mention that many Victorians (something like Fogg in Around the World in Eighty Days) often did not own the books they read. They might have paid a small fee to borrow the newest volume of a popular novel from a circulating library, so that a single copy might circulate among interested readers. They might also take advantage of the collection of a social club, scientific organization, or a lending library. We see this with Fogg: “There was no study, nor were there books, which would have been quite useless to Mr. Fogg; for at the Reform two libraries, one of general literature and the other of law and politics, were at his service.” However, whether Fogg makes use of those libraries seems in doubt, since we are also told “His sole pastimes were reading the papers and playing whist,” and we see him busily reading newspapers as the story progresses, such as in chapter 3 and 20. The idea that newspapers and cards were his only pastimes reveals that he is obsessed with what is new. The club was not only a social connection for the middle- and upper-class gentleman but also a place he could spend an entire day, particularly if he were wealthy (as Fogg certainly is). We see him take his breakfast at the Reform Club (at almost noon! going to bed and rising late were signs of gentility, since a gentleman did not have to wake up to work and was able to afford candles, gas, or electricity to stay up late), read newspapers for hours, and then take his dinner there, too. Fogg’s abiding interest in keeping up with the latest news (as the conversation about the robbery, and his keen interest in travel times, show), again, is absolutely part of his character. That he does not have a study, let alone a library, is interesting, but not out of character: having a good collection of books was a sign of taste and a visible display of wealth, not to mention a useful way to strengthen social connections by lending books or reading together. Fogg, however, as a wealthy and slightly eccentric bachelor whose social circle seems limited to the club, pretty clearly has no use for books at home, socially or personally.

Switching over to Strange Case of Dr Jekyll and Mr Hyde, Poole's comment about not reading extends from books to newspapers, and it would have marked Dr. Jekyll as being very much outside the norm for not only his social class but for Victorian men in general. In the second half of the century, dropping printing costs led to an explosion in the number of periodicals. After the rise of illustrated sensational newspapers in the 1860s like The Penny Illustrated Paper and The Illustrated Police News, which splashed sensationalized crimes and scandals across the cover, and with increasing literacy among the working class, historians consider that at almost every level of society there were people reading, or at least having someone around them who could read to them. In the 1880s, there were thirteen morning and nine evening daily newspapers being sold in London. Reading a newspaper would have been a part of the daily routine of a Victorian gentleman. To not read one would have been to neglect staying up-to-date in current affairs, which might have been seen as failing in his civic duty as a voter and member of the intellectual class. The exact quote from the novel illustrates this well: "The doctor, it appeared, now more than ever confined himself to the cabinet over the laboratory, where he would sometimes even sleep; he was out of spirits, he had grown very silent, he did not read; it seemed as if he had something on his mind." In other words, it is a sign of just how far he has fallen, how obsessed he is, that he neglects even one of the basic activities of a man of his social class.

(I wouldn’t be a literature person if I didn’t mention that the image of reading appears throughout the novel and is one of the most important themes of the text. The accumulation, reading, and interpretation of documents, not to mention the reading of people, is front and center, particularly when we consider that the ability to properly read the relationship between Hyde and Jekyll (to say nothing of the science of “reading” their physiognomy) is the key to solving the “strange case!”)

I can suggest lots of sources if you're interested. A dated one, but a good place to start, is Alan J. Lee's The Origins of the Popular Press in England, 1855-1914, published in 1976. The Flint chapter I mentioned is in The Cambridge Companion to the Victorian Novel, edited by Deirdre David.

(Oh, and a quick edit: With letters to the editor, personals ads, personal and professional announcements, and an assortment of publications geared to enthusiasts of a wide variety of topics, newspapers in many ways did play the role of social media!)