Purchases made in the past are also apparently honoured, regardless of the device used. See below.
Here's the official video launching the re-download feature:
From the press release:
"With this latest Store release, we’ve added a simple way for you to restore content that you purchased and downloaded through Store to your device. We take very seriously the fulfillment of content that is acquired through the Store, and while we can’t prevent certain events that may cause damage or the loss of content, we can make it easier for you to re-acquire it. Please watch this short tutorial below to learn more about how to redownload previously purchased content.
As the tutorial explains, if you use the Store through our mobile client application, you’ll be required to upgrade to the newest version on S60 devices—look for version 1.5(387) or higher—and on Series 40 devices—look for version 1.6.1 or higher—to take advantage of redownloading. The latest version of Ovi store for S60 devices is rolling out now. If you receive a prompt to update your client, please accept it!
If you shop the Store through our mobile web site at store.ovi.com on your Nokia mobile browser, the feature is enabled today. And regardless of how you shop the Store, we will honor purchases made before this new version, so if you purchased the BlockGO game in August and it didn’t download properly, give it another shot by visiting the My Stuff section of the store.
We hope content redownloading will improve the way you use and enjoy content acquired through the Store by providing a simple, easy, and no-hassle way to make you and your content whole again.
We also updated our search experience, making it easier to access what you’re looking for across our entire content catalog. We highly value your feedback, so let us know what you think."