STM32 interrupt and input on same pin
There are as many ways to do it as people can think of.
Your way will work just fine, although it is not very sophisticated as the MCU will be sitting in the interrupt waiting for the bytes to get transferred before exiting the interrupt. If that is all that is needed, it is simple and effective.
The other solution you found is one of the most complex solutions, although libraries make it easy to do. It simply disables the EXTI interrupt and starts a DMA driven transfer and will immediately exit the interrupt to return do what it was doing. The data is transferred in the background and when the bytes are finished, the transfer complete interrupt will then re-enables the EXTI interrupt.
A solution between these would maybe start an interrupt driven SPI transfer in the EXTI and would re-enable EXTI when bytes are transferred.
There are many other solutions too, just pick one that suita your program flow and gets the job done without adding roo much complexity.