MexicanTrain.Online is meant to accompany existing chat and video programs. I recommend Zoom, Skype or Facebook video. Start a call in one of those apps, then come over to mexicantrain.online and start a game.
Reordering tiles only works on larger screens. For example, you can reorder your tiles on an iPad horizontally, but not vertically. And definitely not on phones. Sorry, this is a limitation of the tech.