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It's the classic time-domain equation after the Laplace transform, Z-transform, Euler's and more to simplify things in the freq. domain, then convert back to the time-domain and end up with a simple equation, as far as embedded systems math. There is recursion, it reminds me of an IIR in that the previous output and inputs are used. The PID (not PI only) equation goes back using two previous values.

There is no Ki or Kp that I could see. I consider those terms lost in the math - for example, it's a single "K" Amplification Factor in both terms.