>*The gassy emissions **from** these giant dinosaurs may have been enough to warm the Earth*

I would argue that to replace *from* with *by* would render the sentence ungrammatical. Here are my reasons:

First things first, it should be noted that the word *emissions* here does not mean "an act or instance of emitting" but it means "substances discharged into the air (as by a smokestack or an automobile engine)". [Merriam-Webster][1] That's why the word is in the plural. 

As a matter of fact, the word *emissions* here refers to *methane*, which word has shown up about 13 times throughout the article (including in its title "Dinosaur Farts, Prehistoric Climate Change Linked In New Methane Gas Study"). There is another appearance of the word *emissions* in the article (*The real question is, did these dinosaur's gassy emissions warm the planet?*), where the word *emissions* also refers to *methane*.

Now that the word *emissions* here denotes not an action or event but a substance, the issue boils down to whether the following sentence is grammatical:

>*The gassy substance **by** these giant dinosaurs may have been enough to warm the Earth*

And it's apparent that this is not grammatical. At least not in the intended meaning of the original sentence.



  [1]: http://www.merriam-webster.com/dictionary/emission