Can I run old versions of (now incompatible) apps on MacBook Air?

A bunch of apps require an M1 chip when you try to download from the App Store.

Specifically, I'm asking about Classplus. https://apps.apple.com/in/app/classplus/id1324522260
I'm pretty sure it's not an iOS app that's using the M1 chip; its first update was on 3 June 2020. My MacOS version is Big Sur 11.2

Is there a way to download an older version that doesn't require the M1 chip?

Apple currently recommends that developers make Universal Binaries for BOTH CPU types. Are you sure that apps only support the M1 CPU and don't work on Intel? Can you give us some examples?

They may be advertising that they will work natively on M1, but I would still expect all Mac App Store apps to support Intel CPUs.

EDIT: The app is an iOS app, which previously would only run on iPads or iPhones. The new M1 Macs can also run these apps. It's unlikely that there was ever an Intel version of this app (as there are no Intel i-devices).

The app you linked is in fact an iOS app, and as such requires an M1 chip. Its most recent update was March 2021.