Hi,
There are a number of chips that use this technique or a similar, simpler technique. The main idea is to pump the inductor with enough energy so that when it discharges it provides enough of a boost to get to the required level of voltage at the required current and that is able to happen when the inductor gets to a preset current level. There is feedback, but it's not the typical error amp loop like we normally see because it is assumed that the regulation control does not have to be that accurate and that several operating parameters are nearly constant.
The problem of course is that there is no regulating feedback, only inductor current limiting. Without feedback the circuit will not regulate very well when external parameters change such as load and input voltage.
There are other types of control however, that do not involve feedback but are actually feed forward. That is, they measure something about the circuit before the control stage and vary the control stage based on assumptions about the circuit such as power losses. In the case of the max current controlled inductor scheme, measuring the input voltage allows the circuit to change the control to the inductor to at least partially make up for the changing input. This can make a big difference because now we can adjust the output based on input voltage, at least to some degree of accuracy, without having to directly measure the output itself. This eliminates the feedback loop and thus the problem with the right hand plane pole and other problems that plague boost converters. The drawback is the control is not as accurate so it is best for loads that do not require super accurate current or voltage levels to operate properly.
The first chip you linked to appears to be using this kind of scheme. I have not looked at the second link yet.
So you see this kind of controller is best for loads that do not require super accurate outputs like LED drivers.