This doesn't answer your question, but you should be aware that you don't need to have an Ancestry subscription to view the Ancestry Card Catalog. Once your subscription lapses, your account should revert to a Guest status. You can see this by viewing your account -- it looks like this:

By searching in the Ancestry Card Catalog, you can view the page for that specific database, and read the information underneath the search form. Let's look at the information you would have seen if you had clicked the Learn More link before you made your screenshot:

As you've already noted, both the Source Information and the About the Database sections are annoyingly bare. So the best thing to do is to search for other ways to access Rhode Island Vital Records on the web.
One such option is in the earlier answer but can we find more? Try looking for finding aids as well as looking for the records themselves.
One of the databases at NEHGS is Rhode Island: Vital Records, 1636-1850. Their about the database says:
Description
In 1891, James N. Arnold began publishing a series of vital records
books for the towns of Rhode Island. The series would go on to include
church records and newspaper records, ultimately filling twenty-one
volumes with information. This re-indexing of our original 2002
database includes records from Volumes 1-12.
All 21 volumes are available for viewing at the NEHGS Research
Library, call number F78.A75. Search Tips
SEARCH for MAIDEN NAMES IN FIRST NAME FIELD. Search for spouses and/or
parents names IN THE KEYWORDS FIELD.
But what if you don't have a NEHGS membership, and the database is not currently available to Registered Guest users? There are two things you can do.
- Sign up for the NEHGS newsletter so you will get news of promotions -- sometimes NEHGS offers free access to an entire state's records to encourage users to explore the site.
- Look for the vital records books cited above in other libraries, like the Family History Library in Salt Lake City (note: some books may be viewable at your local FHC; others may be available for you to download), or use WorldCat to find the book in a library near you.
- Because of the age of the books, you may be able to find scanned copies at digital libraries like Google Books, the Internet Archive, or Hathi Trust.
But you don't want to stop at this printed work. You want to get the original image if you can. How do you do that?
NEHGS's guide Using Arnold’s Vital Record of Rhode Island — In Print and Online has the answer:
Whether you use the printed or online version of Arnold’s set, you
should always return to the original documents for the specific towns.
There are many discrepancies in the original Arnold transcriptions.
There is evidence of spelling changes and misinterpretation of the
family data presented in the town records. It is not necessary to
travel to Rhode Island to access the town documents. While the
original records are available on microfilm at the Rhode Island
Historical Society Library (121 Hope St, Providence, RI, 02906), these
reels can also be ordered directly through the Family History
Libraries of the Church of Latter-day Saints or via the NEHGS library.
Use their website to find the appropriate reel numbers.
However, FamilySearch is discontinuing microfilm distribution:
On September 1, 2017, FamilySearch will discontinue its microfilm
distribution services. (The last day to order microfilm will be on
August 31, 2017.)
We know from the previous answer that the images are online, but if they were not (or if their image is not very readable), the NEGHS/AmericanAncestors.org research guide gives your other options for viewing the microfilm, and the FamilySearch Wiki article tells you where you can write the state of Rhode Island.
Searching for 1879 marriages in findmypast's US Marriages Collection gives 8,239 results. If I search for Mary Gomersall, I get three hits, all of which cite FamilySearch microfilms -- two different FHL film numbers. Going back to the FamilySearch catalog and entering the film numbers will show you the film notes, which will give more insight into the nature of the records.
- film 2364529 (cited in the earlier answer) is part of Births 1886-1902 and marriages 1885-1902, returns of births and marriages 1900-1902 (Pawtucket, R.I.) from Pawtucket (Rhode Island). Town Clerk (Main Author), published in 1996 and 2003, and contains "Marriage records v. 4 ( 1902, from p. 247) ; returns of marriage: 1900 ; 1901"
- one search result from film 001845636, which is part of Providence, Rhode Island : births (1876-1890), marriages (1870-1891), and deaths (1880-1892), from Providence (Rhode Island). City Registrar (Main Author), and contains "Marriages : v. 10 (1870-1873), v. 11 (1873-1876), v. 12 (1876-1879)". This film is available to view online but is not yet indexed and must be browsed (camera icon only).
- two search results from film 001822995, which is part of Vital records & indexes for births, deaths, and marriages, 1853 through 1900 from Rhode Island. Division of Vital Records (Main Author) and consists of "MARRIAGES Vols. 26-28: 1879-1881". The images for this microfilm are available at a FHC and presumably to people with an LDS account -- clicking the camera icon results in this message:

On findmypast, the image from film 001845636 shows a register book with the headers "Marriages registered in the city of Providence city register for the year ending December 31st, 1879.". We can get a hint about the equivalent record at FamilySearch by examining the URL:
http://search.findmypast.com/record?id=https%3a%2f%2ffamilysearch.org%2fpal%3a%2fmm9.3.1%2fth-909-49345-26611-71&parentid=us%2ffs%2fm%2f075985370%2f2&highlights=%22%22
Note that the old PAL number is encoded in the code. See https://genealogy.stackexchange.com/a/4154/1006 for a discussion of identifiers, including PAL, FamilySearch's article on Persistent identifiers, and Wikipedia: Archival Reference Key for more information on ARK.
Adding information from the comments:
I tried browsing Film 1845636 but had difficulty finding the waypoint for the register books. However, the image is there:
Rhode Island, Vital records, 1846-1898, 1901-1953," database with
images, FamilySearch
(https://familysearch.org/ark:/61903/3:1:3Q9M-C955-R1KT?cc=1935767&wc=7CWR-B83%3A1590162406
: accessed 29 July 2017), 004146235 > image 739 of 781; Rhode Island
State Archives, Providence.
Note that this register book says who performed the marriage -- that gives you a pointer to church records.
Presumably one of the hits from Film 001822995 is the index and the other is the register (the state's copy, rather than the city copy which is the one on Film 001845636). This is why we're supposed to check all jurisdictions.