Here's a historical look at the Linux market share on Steam, gathered using Valve's publicly provided data. Be sure to look over all the information, don't just take the first chart. If you have feedback, email us any time.

Note: Valve reported on October 4th 2018, that the Steam Survey had a rounding error with smaller distributions not being counted. On top of that, they also fixed another flaw in May 2018 where Windows 7 in cyber cafes was being over counted. Since Valve don't show any historical data, we don't know how accurate the figures are before September 2018 (which has been corrected).

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This is to show how the rise of Asia has clearly impacted the shown Linux market share on Steam.

There's no ideal way to know this. We don't know the total number of users on Steam, sadly Valve rarely give that information out. However, we do know the current record for concurrent online users, which is: 18,528,722 from January 2018.

Using the data we have for January 2018 (0.25%), how many Linux users may have been online at that time?
Linux online total: 46,321

To be clear, that's how many Linux users could have actually been online at that time.

As for an estimation of the total number of Linux users on Steam? Valve reported they had 125 million "active" Steam users back in 2015, considering Valve's rate of growth let's put that at 150 million active users now. Using the latest months recorded share (Sep-2018 - 0.78%), as shown in the last chart above that could equal:
Linux user total: 1,170,000
This is probably wildly wrong, as we have no idea what the active user count is on Steam. Once we get an up to date figure from Valve, we can update this.