You screenshot doesn't show how you achieved this or that you're even using Linux. There is no option to start a secret chat for me on a right click. Where did you download your client?
I am using telegram-desktop from aur, I clicked the three dots (…) at the top next to the magnifying glass, then info (i) to get to the profile, then there is a “more” (…) button where there was a “Secret” option.