Here are the locations included in the list as well as their building styles and current statuses, as deduced by a couple hours poking around on Google Maps:
MISSOURI
12750 Manchester, Des Peres, MO
--Unclear where to place this one. It's possible that it was part of the West County Center mall, which was demolished and rebuilt in 2001-02.
Big Bend & Hwy 141, Twin Oaks, MO
--Kroger Sav-On store with rounded corners; still stands in original condition. Most recently a Schnucks, but now vacant.
Clayton & Clarkson, Ellisville, MO
--Superstore; now a Savers thrift store. Painted and remodeled, but still recognizable.
Gravois at Mackenzie, Affton, MO
--Kroger Sav-On store with rounded corners; now an O'Reilly auto parts store.
Hwy 141 at Hwy 67, Arnold, MO
--Unclear where to place this one; none of the nearby buildings look obviously like a Kroger.
235 Hwy 175, O'Fallon, MO
--Kroger Sav-On store with rounded corners; most recently a thrift store, now vacant. Street is now known as "Veterans Memorial Parkway."
2021 Independence, Cape Girardeau, MO
--Might have been a Family Center. Demolished and replaced by a Walmart Neighborhood Market.
2306 Missouri Blvd, Jefferson City, MO
--What appears to have been a Superstore that was subsumed into an adjacent Kmart as an addition. Looks very odd, with the scars of the canopy still clearly visible on the facade.
ILLINOIS
200 N Grand, Springfield, IL
--An unusual facade with widely-spaced vertical channels (wider than those on a Superstore) makes me wonder if this was also built as a Kroger Family Center. Now remodeled, and selling groceries as a Shop 'n Save supermarket.
1755 Wabash, Springfield, IL
--A Shop 'n Save supermarket now stands on the site, but it appears to be a new building.
1216 S 2nd, Springfield, IL
--Appears to have been demolished. A 3-story state office building now stands on the block.
1501 S Dirksen Pkwy, Springfield, IL
--Kroger Sav-On store with rounded corners; still selling groceries as a Shop 'n Save supermarket. A more elaborate facade has been tacked on to part of the front.
3013 N Sterling, Peoria, IL
--Superstore; still stands in original (albeit painted) condition as Big Lots. The shopping center is architecturally homogenous, and has a second set of superstore arches over the walkway at the opposite end.
901 West Lake, Peoria, IL
--This address was later the site of an experimental Kmart (now closed) with
creepy green faces.
A Kroger still stands on an outlot at 801 West Lake, but it looks modern and does not appear to be the 1979-era store.
3103 W Harmon Hwy, Peoria, IL
--Still a Kroger today, but refronted and renovated beyond recognition.
1405 W Garfield, Bartonville, IL
--Superstore (probably a SupeRx combination) that's still a Kroger store today. The facade has been extensively remodeled, but some of the original columns are still intact. An unusual texture of decorative blocks is visible on the side wall.
900 South Main, E Peoria, IL
--1950s-era store with an expansion visible overhead; now home to a window and siding company.
2321 N Wisconsin, Peoria, IL
--A Kroger still stands on the site today, but it's been either rebuilt or refronted and renovated beyond recognition. Part of the adjacent shopping center still retains superstore-style columns, and another part retains a circa-1960 look...making the property look like a Frankenstein.
30th & Broadway, Quincy, IL
--Unclear. A Staples store and a vacant supermarket-size store stand on opposite sides of the street, but neither looks like a Kroger to me.
2811 Belt Line East, Alton, IL
--Kroger Sav-On store with rounded corners; still stands in original condition selling groceries as a Schnucks supermarket. Street is now known as "Homer M. Adams Parkway."
5771 Godfrey Rd, Godfrey, IL
--Superstore; still stands in original condition.
This store's fate is an interesting case. I surmise that it closed as a Kroger when the St. Louis division was shuttered in the 1980s. Then it spent time as an independent market, then it spent time with a non-grocery tenant, then it went vacant...then it reopened in 2015 as a Ruler Foods store. Ruler Foods is a Kroger subsidiary, so Kroger was reunited with its superstore after a several-decade hiatus!
A picture of the building is available
here.
655 Berkshire, E Alton, IL
--1950s-era red brick store. Stands vacant in original condition.
1901 E Edwardsville Rd, Wood River, IL
--Possibly built as a Family Center, judging by the massive footprint? Appears to have been gutted and renovated beyond recognition.
Rt 13 East, Carbondale, IL
--Former superstore that opened on August 15, 1976 (according to archived newspapers); appears to have been demolished and replaced by new development. An adjacent part of the shopping center still retains superstore-style columns.
1818 Walnut, Murphysboro, IL
--1950s-era store. Now houses the Murphysboro Youth & Recreation Center, with a park where part of the parking lot used to be.
1609 S Park Ave, Herrin, IL
--Still a Kroger store today, but refronted and renovated beyond recognition.
1112 N Carbon St, Marion, IL
--Superstore; now an AutoZone store. Painted and remodeled, but still clearly recognizable.
I'm surprised that Kroger built so many rounded-corner Sav-On stores in Missouri and downstate Illinois in the late 1970s. Maybe they considered the food-drug combination concept to be their Hail Mary pass for market-share recovery, before giving up on many of those markets? Who knows.
I know that Schnucks ended up with a fair number of the St. Louis stores (via National), and the Springfield, Illinois stores all seem to have ultimately gone to SuperValu's Shop 'n Save subsidiary. Peoria is the only metropolitan area on the list that still has a strong Kroger presence today.
I drive through downstate Illinois at least once a year, so I may eventually scout out pictures of some of these store locations.