How do I mark all podcast episodes as played in iOS10? I tried looking this up but there are only examples for previous versions of iOS where there was an option in the podcast settings called "mark all as played".

This option is not there anymore. Is it gone forever?
Marking all podcasts as played

This feature was originally removed sometime during iOS 7 (I think iOS 7.1, but am not certain on this).

Just in case you're not aware, the closest option to doing this within the builtin Podcasts app is to do as follows:


Launch the Podcasts app
Tap on My Podcasts
Tap on the Podcast series you want to mark as played
Tap on Edit (located at top right corner)
Now tap on the radio buttons on the left of each episode
Tap on the Mark option at bottom left
Select the Mark as Played option


This will mark all your selected podcasts as played.

Of course, you can also use iTunes to mark them all as played and then sync your iPhone, but that may only be quicker overall if you wanted to mark multiple series of podcasts as played. Otherwise the above steps will most likely be more convenient - although certainly not as convenient as the older Mark all as Played option in earlier generations of iOS.

Gone forever?

In terms of whether this feature is gone forever, no-one here (or even at Apple) can answer that. There's no telling what may or may not happen with the Podcasts app in future.

Alternatives
Finally, there are a number of very popular third party podcast apps which many users have turned to. It may be worth you investigating some of these to see if they're suitable for your needs. I list a few below (some are free, others aren't):


Overcast
Pocket Casts
Downcast
iCatcher! Podcast player
Pod Wrangler


Note: I am not affiliated with any of the above apps in any way.