I downloaded the apk from here with WhatsApp version 2.17.106 (size 34601974 bytes). There, it says: "Android OS 2.3.3 or above". I can extract the APK's contents without errors, so the file is not broken.
My old smartphone model is GT-S6102, a Samsung Galaxy Duos, running Android 2.3.6.
I have enabled "Install from unknown sources" and "USB debugging". I have let Lookout scan it before installing.
When trying to install that APK using the file manager, I get this message:
There is a problem parsing the package
I am also unable to install it from Google Play Store. From Google Play, it says "Package file is invalid".
Update: version 2.17.350 does not work again.