Looking closer at the (lower) op-amp and its voltage gain, I ended up with something in the form of:
$$V_o=a V_i + b$$
So the gain is dependent on the input voltage, not a neat constant. 
... moreover, the formula you wrote does not include such a dependency.
$$V_o / V_i = a + b / V_i $$
Thanks for taking the time to illustrate with an LTspice simulation, which I should development a habit of using...
I have a very specific question here:There is a 0.7mA current source shown in the block diagram, replicated in this isolated subcircuit.

How would this current source affect the behaviour of this circuit? Suppose the voltage on the inverting input is also Vo/2, will this current be drawn through RF, or from the output of the op-amp, or a combination of both?
My guess is, since the ideal opamp has 0 output impedance, and has its power source, this 0.7mA current will entirely be sourced from the opamp. The problem with this is then, if so, with or without it, there will be no difference to the whole circuit (or the IC), which is impossible to be true, so would disprove my understanding. But why?
(Except for this last question, I think I've understood the working of this IC at the block diagram level. Thanks to @ommsiva for starting this topic.)
[Edit: more thoughts on the above question – I think my guess is probably the correct answer, assuming no voltage drop across the diodes. This means that the 0.7mA current source is solely due to the two diodes (otherwise would not be needed). But thoughts are welcome.]
[More edit: I figured out – assuming ideal diodes with 0V voltage drop, the 0.7mA current source only turns the otherwise source-only opamp back into its dual mode, i.e. source and sink, but with a 0.7mA ceiling for the sink mode. There will be sight difference from this due to non-ideal diode (and opamp), but the general principle and design intention should remain. But now I also realised a conceptual error in the block diagram: The output of the two opamps is internally connected to ground only though the 0.7mA current source. This must not be the case because if so, voltage on Pin 3, i.e. the input to the internal PWM comparator, would always be 0V. One option for the correction would be omitting the ground symbol on the left side of the current source.]