In Google Chrome, how do I drag things around on a touchscreen Android device?
You can do it with just a mouse (or pen) on pages where it is supported. I tested it with a plain USB mouse on my Moto G running Android 4.4.4.

I resized area for post with bottom right striped triangle on "dotaz nebo sdělení" field with mouse. See this tested page.

Or you can pair an ordinary Bluetooth mouse with your device. Probably any modern Android device includes Bluetooth mouse support.