Is this available online anywhere?
Yes, these documents with images are available online in the subscription service Ancestry.com, where it is called "1890 Veterans Schedules" under the Census and Voter category when you search for a person or under United States 1890 Veterans Schedules as a separate database in Ancestry's Card Catalogue.
The records are also available on the free service
www.familysearch.org.
The record did not come up here when I searched "Edward W Ryan", my subject, by name, at least I didn't see it, but the file is searchable as a separate database entitled "United States Census of Union Veterans and Widows of the Civil War 1890", its official name. Find this database by selecting Search on the entry menu bar when you first go to the site and then under the map of the world at the right (on a computer, not a mobile), below "Find a Collection", fill in the title above quoted in the search box just above "browse all published collections". Don't worry you don't have to browse anything. On the next screen, a search box for your subject person will come up with the database. When I filled this in and searched, Edward Ryan's record came up just as shown on civilwartalk (that copy was from Ancestry). BTW on my successful search, I did not fill in a residence or date, because when I tried that, the name did not come up, so leave those boxes blank.
I had not realized before accessing the files through familysearch.org that the 1890 Veterans' census was confined to Union Veterans and their widows because it was needed to forecast federal Civil War pension obligations. Confederates thus are absent from the list. The widow will come up with a search of the soldier's name.
Another comment, when the states canvassed residents for this compilation, some of them published their own results as a state collection and some asked questions of their own, such as do you belong to a GAR Post, were you taken prisoner, are you dependent for your support, and were you injured, wounded or diseased during the War. These questions were in the Kansas compilation known online on Ancestry.com as "Kansas 1889 Enrollment of Civil War Veterans" under the military category. If you have an ACW vet in KS in 1889, it's helpful, and KS also has incomplete but plentiful GAR post records on Ancestry under the "military" category if you want to see that. Widows are listed in these KS records as well. If you don't see such a database for your State, try contacting the State archives or the state historical society for further information.