Clearly I will lose the heat that would otherwise enter the room through the window if I hadn't blocked it with the Solar Venti as opposed to my mounting it on an outside wall.
The heat you're talking about losing here is the majority of the heat available in the light that enters the room. Note that a lot of heat potential has already been lost once you are working with light that enters the room because of the reflective properties of the windows you're working with. There are many different kinds of windows with many different reflective properties but all windows are going to reflect some of the incident light and some of them might reflect quite a bit of it. When the device is outside, this doesn't matter. When it is inside, it is working with a much reduced potential.
I assume the light-facing part of the device is a matte black to maximize heat gain from exposure to sunlight. The only additional heat you will gain from this setup is the difference between the heat gain of the device and the heat gain of the objects in the room the light would otherwise have struck and partially reflected off of and back out a window.
It's difficult to estimate what that difference is going to be because it will depend on the objects in the room, their positions, the location of various windows, etc.
However, it's likely to be a small difference because many of the objects are probably not highly reflective and if they are they will probably reflect a lot of light onto other objects inside the room, not outside.
The device itself will contribute some heat to the room since it appears to have an electric fan. If this is the case, the power to drive the fan will dissipate as heat and warm the room. Of course, you're paying for the electricity for this resistance heat so it's not really a win.
Finally, the device will do some work moving that heat into the air in the room. This is the easiest place for it to stratify and end up at the ceiling where you will mostly not be able to appreciate it. If there is a living space above this room, people walking on the floor in that space may appreciate the extra heat though. However, in the air, it will probably also quickly leave the building due to unintentional or intentional air changes required for healthy air quality.
Contrary to this, if you let the sunlight heat the objects in the room, the heat will be available to anyone in contact with those objects - for example, someone who sits in a chair or walks on a floor which has been warmed. Also, the heat will remain in the living space somewhat longer because it will have to radiate away from these objects and warm the air before it can be carried outside - or radiate and warm a wall which can then radiate it outside.
Thus, use of the device in the proposed manner seems like a wash or a slight loss.