Seems Valve are on a bit of a roll lately fixing up some long-standing issues in the Steam Client for Linux.
They've been releasing quite a number of Beta client updates recently with Linux improvements, like the one last week which had a fix for a this two year old issue where you were unable to move games around if they had files bigger than 2GB.
The latest Beta, released today, fixes another long-standing issue with gamepad Rumble support. Valve said they "Added support for rumble pass-through for virtual controllers. This fixes missing rumble support for any controllers opted into Steam Input, and rumble emulation support for the Steam controller.".
Speaking about it on Twitter, Valve developer Pierre-Loup Griffais said "Today's Steam client update adds support for rumble for emulated controllers; this required working around a kernel bug, which we're also fixing upstream: https://www.spinics.net/lists/linux-input/msg61613.html".
Happy to see this getting attention, as someone who makes heavy use of their Steam Controller. Although testing a few games earlier with it turned on (DiRT 4, Bastion, Rocket League, BallisticNG) it still didn't give me any Rumble oddly. Possible I'm missing something as I've seen reports of it working sometimes for others.