No, the reason they made their engine and IDE free is to cater to indie developers, hobbyists, and students. Unity is to these people now what Flash used to be ten years ago—an initially simple but ultimately powerful game-making tool. And the small percentage of those that graduate beyond just doing it as a hobby or experiment end up sticking with the tools they know. It's a very bottom-up approach to the market.

Remember also that they offer a Pro version that costs money, and that they restrict the use of the free version to companies that make less than $100k per year.

There are a lot of people wanting to get into game-making these days, since tools have gotten better and the indie market has proven its worth. It's telling that Epic is putting even more emphasis on their tools than their games these days. In a gold rush, as it's said, the ones that get rich are the ones selling pickaxes.

I know, I actually started developing with the Unity engine for a side project about 6 months ago (I'm primarily a web developer with no previous game-dev experience).

The fact though is that you can publish commercially (even to mobile app stores) without a Pro license. The reason why making the base version free is commercially viable for them (aside from their hope that some users upgrade to Pro) is because of the success of their asset store.

Pretty much all Unity developers spend money on the asset store even if they're on the free plan. I myself have spent a few hundred dollars on the asset store of which Unity gets a cut thus allowing them to immediately monetize their free users.

It'd be interesting to know what proportion of their revenue the Asset Store accounts for. My own guess is very little compared to the revenue from licensing Unity itself. When a 20-person company licenses Unity Pro with iOS/Android support and the Asset Server, that's either $100,000 in licenses up front (plus upgrades later), or $2450/mo for the subscription option. And there are quite a few companies that size (not to mention bigger). I would be surprised if Asset Store revenue is really rivaling that. Hence my guess is that the free version of Unity is mainly intended as a "freemium" product to drive later sales of the Pro version.

Yep indeed. Unity3d has this for a long while.