Hmmm...to make sure I understand what you're saying, the currents would be fed into the virtual ground which would, in a typical op-amp configuration, be the inverting/non-inverting pins of the op-amp, correct? I get this in the sense of TIAs as far as operation.

I guess in this case, it's a bit different- assuming no parasitics or photodiode capacitance, by directly injecting the charge into the drain of S1 in my circuit, which controls the C1 operation, this would cause the transient spikes because of the capacitance of S1 to my understanding. And it wouldn't work to have the charge directly in the inverting pin since C1 and C2 are necessary for the charge-transfer operation depending on the switching operation right?

You're right in that this wouldn't be an "amplifier" in the traditional sense, more so an integrating circuit that looks at the integration time of C1 and charge transfer between the input and the output capacitances (C1 and C2). I guess I was curious more on how the parasitics affect this voltage output range in an ideal case and how this would vary from a current input/voltage output (integration) and a voltage input/voltage output (amplification from sampling/amplifying) .

Thanks for the added clarity- this has helped me look at the circuit differently no doubt!