How do I achieve dynamic shadows in a 2d game like Thomas was alone

How do I get shadows in my 2d game like the ones in Thomas was alone? There is a video demonstrating what I mean right here

In Thomas Was Alone, the game was rendered in 3D, despite appearing 2D, which meant it was easy to cast shadows. Red Blob Games (as always) has some really awesome information and tutorials on how to achieve this effect in 2D:
http://www.redblobgames.com/articles/visibility/
http://simblob.blogspot.com.au/2012/07/2d-visibility.html

Actually, Mike Bithell recently tweeted that he did the lighting in TWA “stupidly” - using planes and moving their vertices based on lighting calculations

https://mobile.twitter.com/mikeBithell/status/462194109588193280

update:
Seeing as this thread has resurfaced nearly three years later, I’ll point out that there are now plenty of free (and, even better, open source) alternatives. A quick search of “Unity 2D dynamic lighting” on GitHub will produce gems like this, for example: GitHub - f15gdsy/2D-Light-of-Sight-Unity: A plugin for creating 2D lighting & shadows, and line of sight effects in Unity3d.

The Asset store can certainly help here if you don’t want to spend a lot of effort:

(Kind of a shameless plug as we wrote Super Fast Soft Shadows on that list)

If you are looking for another option to implement it yourself, I’m a big fan of this method, and it sounds like it’s the same one as Thomas Was Alone according to tanoshimi:

I’ve been using the hard shadow method for over a decade with great results. You can trivially perform the shadow projection with a matrix. SFSS is an extension of the hard shadow algorithm with some shaders to render the penumbras accurately instead of using the finicky/tedious/innacurate shadow fins from that article.