Did Humble Bundle stop supporting the "Activate on Steam" option?

Essentially, yes.
According to this Humble Mumble blog post, they have stated that they'll be removing OAuth support for Steam, which is the main method of redeeming keys through a third-party/link.

And that all purchases made before the 12^th of January 2015 can still use this method up to around the start of Febuary. Anything bought after the 12^th or is unredeemed by the start of Febuary will be converted into actual usable keys... Codes.

So why?
Nobody knows; Steam has not released an official announcement.. Not that I could find (or even remember seeing popping up in my Steam news feed) anyway, but it's open to speculation on Reddit.

Update:
To remedy this, Steam has (around a year ago at the time of this edit) has permitted key redemption through the web browser here.

You can pre-fill the key to add a query with the key key in the URL:

https://store.steampowered.com/account/registerkey?key=AAAAA-BBBBB-CCCCC  
https://store.steampowered.com/account/registerkey?key=AAAAA-BBBBB-CCCCC-DDDDD-EEEEE
https://store.steampowered.com/account/registerkey?key=237ABCDGHJLPRST%2023
https://store.steampowered.com/account/registerkey?key=This%20is%20definitely%20not%20a%20key

As mentioned, yes Valve stopped Humble Bundle offering this functionality a long time ago. However, I've created an open-source Chrome plugin, Steam Redeem, that attempts to recreate this behaviour.

Basically once installed it detects Humble Bundle keys in your browser and injects a redeem button. When you press the button it uses the Steam browser API (accessible manually at https://store.steampowered.com/account/registerkey) to redeem your steam key. There's also built-in bulk redemption, if you click the Steam Redeem logo (next to your address bar) it will automatically redeem all keys visible on the page.

It's a work in progress, and being open source, contributions are welcome.

To follow up, for future querents, Valve began offering web-based activation of keys again in August 2017, and Humble Bundle employs this by providing a button that brings up that page with the key filled in. If you are already logged into Steam, it's essentially a three-click process. Once on the Humble Site to Reedem on Steam, one to accept the Steam agreement, and then one to Redeem. This is, of course, substantially similar to the plugin that Benjamin apparently created. I don't know whether they employed his code, or just rolled their own, similar, solution.