I have an online friend from the other side of the globe. We met in chess.com. But I'd like to try a different game this time. We are not console gamers, but have smartphones. Are there any online games we can try for free that can be played real-time? Looking for something light and can be played in the phone browser.
Definitely the opposite of "light", but you mentioned chess and if you're into something similar but very different, you might try learning #Go together on online-go.com. That site has a very short introduction into the game under the Learn tab, but it only covers the very basics and initially you will have no idea what you're doing. The rules are simple, but there is a lot of complexity that arises from that and professionals study the game for years. But even as a complete beginner it's fun. Full on 19x19 games can take a long time, but games on a 9x9 board are fairly quick, comparable to a chess game.
Still, this would be a journey. If you want something not turn-based and relaxing to play while chatting maybe try something else but I can't give any recommendations.
I second the recommendation of Go. I'm very much a beginner, but the subtlety and variety of every game kind of ruined chess for me.
Some more recommendations of learning or beginner resources:
Go Magic has a lot of really in depth video and interactive tutorials. There's a paid plan, but the beginner and early intermediate courses are free and way more thorough than anything else online right now.
The Conquest of Go is a great little game on steam that has its own tutorials and a campaign mode with scaling difficulty. It's my favorite way to play against bots, but you can also connect your OGS account and play online through there.