That goes back to Ken Thompson's NFA regex interpreter from 1968 [1], [2], [3]. Note: that whole regex series by Russ Cox [4] is great.

[1] https://dl.acm.org/doi/10.1145/363347.363387 -- Programming Techniques: Regular expression search algorithm

[2] https://swtch.com/~rsc/regexp/regexp1.html -- Regular Expression Matching Can Be Simple And Fast

[3] https://swtch.com/~rsc/regexp/regexp2.html -- Regular Expression Matching: the Virtual Machine Approach

[4] https://swtch.com/~rsc/regexp/ -- Implementing Regular Expressions

I second the Russ Cox recommendation. I read that ages ago and that was what made me realise some theory could actually be useful in practice.