TL;DR: Software is eating the world.
First, it doesn't, but it can be easier or cheaper if you use one. You can build a closed-loop controller using only analog electronics, but it doesn't mean you should. Because silicon is so cheap, sometimes it's reasonable to use a $1 microcontroller and 20 lines of code, instead of 3 opamps, 5 resistors and 3 capacitors. I don't mean that software is always a good idea, but you get my point.
Next, if you want an LCD-based user interface (it doesn't mean you should, you can use an analog potentiometer, but having a display is the norm these days), you need a microcontroller anyway. You need a microcontroller to control the pixels on a screen or the numbers on a seven-segment display, and you also need software to implement functionality such as "press this button to change the temperature", or "save the current settings".
Also, these "novelty" soldering irons can power themselves via USB Type-C by using the USB Power Delivery protocol (it doesn't mean you should, but people are having fun doing it), which is a digital protocol, you definitely need a controller and software to do the handshake in order to get DC power. A single microcontroller can perform this task as well.
Now, does it really need a RISC-V microcontroller, instead of, say, a 8-bit 8051 chip? No. But the target audiences of this soldering iron are hardware tinkers, and previously they already ported things like Tetris and Game of Life to the soldering iron, so... Why not?