get a JSON list of all currently open tabs from your android device
Install Android command line tools on PC
Enable USB debugging on Android device
On the PC execute
adb forward tcp:9222 localabstract:chrome_devtools_remote
Chrome instances expose access to a debugging protocol via a unix domain socket with the abstract address "chrome_devtools_remote"
Read about abstract namespaces and addresses
Executing the adb command listed above will forward requests to port 9222, on to that socket.
You can get a list of all the unix domain sockets on the Android device by typing
adb shell cat /proc/net/unix
The debugging protocol exposes JSON data about the chrome instance over HTTP.
A JSON file listing the open tabs can be retrieved by executing
wget -O tabs.json http://localhost:9222/json/list
Overview of remote debugging in Chrome
lmmx's wiki for android-open-tabs-export via chrome debug console