Yes, these are hard-wired logic and just a handful of bytes for two to four registers (at least input and accumulator registers, everything in BCD). Only more advanced calculators use floating point.
Most of the implementational details would appear to be buried in files on engineering workstations at Chinese factories.
I found a calculator teardown at http://electronupdate.blogspot.com.au/2016/08/reverse-engine... a while ago. The author says it's very old but doesn't provide a ballpark (eg, 1990, 1995, 1998, 2003, etc). It does look quite hairy (and possibly not particularly compactly designed?).
I would guess there's a ridiculously simple ALU somewhere in there, but I wonder what else is involved in the specific context of a high-production-volume fixed-functionality design.
I hope to find something similar for a clock at some point.