I'd recommend Godot.

Unity is also a valid choice, but networking is in a weird state right now with the official APIs, so he'd have to use third-party solutions that integrate with Unity (such as Photon, MLAPI or Mirror). It's not the biggest obstacle, but still an annoyance.

Godot or SDL, or Gamemaker... Depending on his current skills and preferences.

For simple 2D games, I feel that Godot is often a far better choice than Unity. However, I've never used Godot's networking or multiplayer features, so I can't comment on those.

For 2D people generally prefer Godot. There's also https://coronalabs.com/