I think you don't understand how this app actually works.
As I understand it, the app is essentially automating a process which you would do yourself. The app does the exact same things you would do to search for availability, except with no further clicking on your part and filtering the results into a neat matrix.
This is why it needs your log in details, because it is doing exactly what you would be doing yourself, i.e. as part of searching for space, you need to provide your details.
I don't know how AwardNexus works (maybe they have agreements, general operating accounts or direct inventory interrogation - after all, ExpertFlyer and KVS can also get at award inventory) to search for availability, but clearly they have a more sophisticated setup than the app here.
I think Wandering Armean has a similar award search facility that this app provides, in that it also needs your account details to basically automate a manual process.
There was a rather popular award search engine that was a hit here; I think it was called Awardtravlr? The main advantage of that one is that it provided deep searches for connecting itineraries, albeit it could work a bit slow. It was shut down eventually; I can't remember the exact reason.
Your understanding is correct. My app automates what you would normally do yourself when searching for an award. If you turn on debug mode, you can see the app performing searches like you would do yourself.
I don't know how AwardNexus does its search - my guess is that it does the same as what my app does but uses a pool of accounts and does the search on its server(s). ExpertFlyer may have some agreements with airlines but my best guess is they scrape sites as well. KVS does the same as what my app does for award searches but it issues raw HTTP requests without actually navigating to the page(s).
I actually created this to automate my personal searches across multiple airlines where I have miles and thought that maybe some people would find it useful.