Github issues are not for support. They are to report real bugs or enhancement requests. Please join the support email list at direwolf@groups.io . That said, page 72 of the Direwolf UserGuide talks about your options including reversing the logic with the "-" option and don't forget that you might want to de-assert DTR when you assert RTS. You need to figure out what your radio really needs.

Thanks so far. Honestly, I cannot tell at the moment where the problem lies. I've done another test with an FTDI FT232R USB-Serial adapter and here it works also with PTT COM5 RTS. But, on the other hand, a serial terminal program which allows to manually set the RTS and DTR line is able to control the IC-705 correctly. As far as I remember it is however based on .NET Framework and it's hard to say what happens under the hood.
I'll do some debugging based on the direwolf code on my own and report the results here.

Finally, I've compared the behaviour to a simple Qt C++ test application and saw that Qt handles DTR and RTS without any problems. I've cross-checked with the QtSerialPort (open)source code and updated the code of the PTT handling accordingly ;-)
It seems to me that the behaviour depends on the implementation of the serial port driver (or even the hardware) how the DTR/RTS lines behave together with Windows.