Unless you mean the extended or master privkey, you can export individual privkeys. In the current version of Electrum, you go into the 'Receive' tab then tap on the address. It will send you to a list of addresses in your wallet. Tap the address you want, then tap 'Details.' Their will be an option to 'Export private key' which will require you to input your passcode first. You can then tap on the privkey and it will be copied to clipboard.
In previous versions of electrum, the address list was in a tab called 'Address' just like the tab 'Receive' or 'Send.'
I have posted screenshots below.




Clearly you haven't been using the right blockexplorers. His adresses do check out in terms of BCH being stored on them.
Also he didn't post his privkey, but an xpub. However you make a fair point. I haven't checked it out, but as far as i am aware, there is no way to access an xpub on the android version of electrum? Or is it just privkeys that you're unable to access?
You can export the master pubkey as well, just not the master privkey. You need to tap the top part, which will take you to the master pubkey and place where you can get seed.

