The speech recognition system uses the standard multimedia device API to get microphone input, as the majority of software would, so this would likely happen with any application that uses the microphone.
I had a look at the setup guide (didn't look like there was a proper manual available, unfortunately), and a few reviews, and this issue/limitation isn't mentioned anywhere that I could find.
You could try checking for firmware updates via Logitech's "Logi Tune" software, just in case they've made a change that would fix this. If not, you'll want to contact them about this
Should none of those provide a solution, and if you have a Bluetooth receiver, you could try connecting the headphones over Bluetooth, to see if the behavior is preferable (though depending on the profiles the device supports, it may not be; credit to Gary for the suggestion)