In the original Pinocchio [GGPR13], the authors didn't use R1CS at all.
As a ZKP friendly computational representation, R1CS was proposed later that year in [BCGTV13] Appendix E. The reduction from an arithmetic circuit to R1CS is quite straightforward, which I guess is the reason why there's no dedicated papers introducing such a computation model.
Soon after its introduction, the BCGTV13 authors started to implement the system into libsnarks, and people started to realise that R1CS is quite easy to be arithmetized. (normally a SNARK is based on Linear IOP or a polynomial IOP that operates on polynomials, thus the efficiency of the arithmetization of R1CS or other representation into polynomials is important).
Ben-Sasson et.al has a pretty good empirical reason on why R1CS became a popular choice in his 2018 Aurora paper (Page 4):
We choose R1CS because it strikes an attractive balance: it generalizes circuits by allowing “native” field arithmetic and having no fan-in/fan-out restrictions, but it is simple enough that one can design efficient argument systems for it. Moreover, R1CS has demonstrated strong empirical value: it underlies real-world systems [Zca] and there are compilers that reduce program executions to it (see [WB15] and references therein). This has led to efforts to standardize R1CS formats across academia and industry [Zks].