I believe I can comment on what the issue is. This is similar to support for example for CEF framework, which is used to plug in a Web interface into a native application. Since these frameworks present a different mechanism of access to their DOM compared to standard browsers, TestComplete cannot access objects - and in fact, even connect to these frameworks.
We have a (rather big) customer who are using CEF 1 as their Web engine of choice, and they are writing a custom extension for TestComplete to support it. So far, they appear to be doing fine with the implementation.
To note, they have not found any other tool thatn TestComplete that would either support CEF, or be extensible enough to implement support for CEF on their own.
I think that is going to be our short-term recommendation to customers who want to use different Web engines for hybrid applications on the desktop. We can support you with some technical assistance in the usual manner. I imagine, such work can also be contracted out.