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I imagine the animation of the text has probably been made in flash, maybe in after effects, and the transtion of each word/block of text was done individually by hand (so to speak) with means of animation paths and modifiers, and not one of a programs preset animations.
Making something like that wouldn't be too complicated if you know what you're doing (ofcourse), however I do not know of any free alteratives to either program, it could perhaps be done in blender, but I wouldn't know where to start in assisting you make the animation. Your best bet would either be trial versions flash/AE and hope you learn how to do it/make it within 30days, study lots of tutorials, or try with blender and study lots of tutorials.
Having just run that video and looked at it carefully, I am reminded of transitions in Powerpoint - it's very like animated transitions.
An alternative way of doing it is to draw each frame ! They are, after all, fairly simple but at 25 frames/second that's a lot of frames ! I did something vaguely similar once, an animated GIF of candle flames on a birthday cake. This was done in a graphics package by drawing the outline of each 'flicker' of the flame and then sequencing them. To avoid the impression of the flames dancing in lock step, I started the sequence for each flame at a different point in the cycle.
Would it be worth your while seeing if you can create video out of a Powerpoint animation ?