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Apparently the recently played list has no concept of what games are actually launched, if you have opted out of playtime tracking.

For the first few months of Galaxy usage I had it enabled, and then disabled it when I became more privacy minded.

Now that I have been 'upgraded' to Galaxy 2.0, the list of recently played games is exclusively what I played two years ago, from that period when playtime tracking was enabled.

Wouldn't it make more sense not to display a recently played list if you don't have sensible information? Its not as if I am going to suddenly return to games I haven't touched in two years, when there are another 200 in my backlog.
I'm having the same problem, except I have playtime tracking enabled.

In my case the "recently played" games are accurate up to the "upgrade" from the 1.2 client to the 2.0 client. Since switching to the 2.0 client "recently played" has not updated at all, either on the "recent' tab or when sorting by recently played in the other tabs.
After several days of not updating at all, my recently played games is a bit more recent. At least, now at the top of the list are games that I have played in the last few days.

But it still isn't updating immediately. If I go into a game and play it it remains where it is in the sorting.

I suspect that recently played information might be entirely cloud based, and the galaxy client downloads it periodically and then updates. I have been getting several error messages about the client not being able to load some information or other, so maybe this is related.