Vital Chek site sez that they get death certs. from 1911: "Death Certificate -
A certified copy of a death record that can typically be used to obtain death benefits, claim insurance proceeds, notify social security and other legal purposes. Death Certificates are available for events that occurred within the State of Kansas from July 1, 1911 to present."
The state of Illinois, on their "Illinois Staewide Death Index, Pre-1916" is a project of the Illinois State Archives - they are checking each county and then creating the index, which is where we find the entry you referenced above. But those records are still held by the county: " The pre–1916 Illinois death index is an ongoing project coordinated by the Illinois State Archives. The sources for this index include original county clerks' death records, such as death registers and licenses. For each death, the index includes the name of the decedent, the date of the death, the name of the county where the death occurred, the place of death within the county, when possible; the age and sex of the decedent and a citation to the original record—volume and page number for death registers or certificate number for death certificates."
Therefore, this tells us that this state-wide index just cites to the original record's location in the specific county. So Vital Chek won't get it for you /the state doesn't hold the record so you gotta get it from Clark Co.:
Clark County Clerk and Registrar
501 Archer Ave.
Marshall, IL 62441
Newspaper entry: JONES, Daniel died in Dolson Township on July 27, of meningitis at the age of 77 years. September 30, 1879, Tuesday, page 4, Clark County Herald.