Removing the battery is the same as opening the switch in this circuit: they both will indicate that the device has been tampered with (output will be low).
I guess there is not enough context but it doesn’t seem particularly novel to me.
If cost isn’t a big factor and you wanted to go big on security then something like this Maxim part would do it. https://datasheets.maximintegrated.com/en/ds/MAX32558.pdf
However if that’s overkill or you’re allergic to Maxim then searching on AVR, PIC, MSP430, Cortex M0 + tamper detect application note should get you a lot of examples.
Depending on the product, microcontroller and mode of operation you might come in on a battery monitor input, a more robust but “digital” external interrupt, a comparator, just an ADC, or something else. Even creative use of built-in voltage regulation can sometimes work.
If you wanted to know if the battery was removed you have simple options like cap up your supply, rapidly switch power modes, save off a bit somewhere before BOD kicks in. Alternatively in some cases you could just use the BOD if your hardware is set up correct.
The linked circuit is fine as a jelly-bean circuit in low volume/low security products and allows you to tick the “tamper detection” box on the cut sheet.