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With the upcoming Vera C.~Rubin Observatory Legacy Survey of Space and Time (LSST), it is expected that only $\sim 0.1\%$ of all transients will be classified spectroscopically. To conduct studies of rare transients, such as Type I superluminous supernovae (SLSNe), we must instead rely on photometric classification. In this vein, here we carry out a pilot study of SLSNe from the Pan-STARRS1 Medium-Deep Survey (PS1-MDS) classified photometrically with our SuperRAENN and Superphot algorithms. We first construct a sub-sample of the photometric sample using a list of simple selection metrics designed to minimize contamination and ensure sufficient data quality for modeling. We then fit the multi-band light curves with a magnetar spin-down model using the Modular Open-Source Fitter for Transients (MOSFiT). Comparing the magnetar engine and ejecta parameter distributions of the photometric sample to those of the PS1-MDS spectroscopic sample and a larger literature spectroscopic sample, we find that these samples are overall consistent, but that the photometric sample extends to slower spins and lower ejecta masses, which correspond to lower luminosity events, as expected for photometric selection. While our PS1-MDS photometric sample is still smaller than the overall SLSN spectroscopic sample, our methodology paves the way to an orders-of-magnitude increase in the SLSN sample in the LSST era through photometric selection and study.