These clips come, of course, from the period after the September 11, 2001 terrorist attack and were a core component of Bush's anti-terrorism rhetoric. This strategy was first laid out in an address to a joint session of Congress on September 20, 2011 (Bush made a similar false dilemma in this address which can be found on page 5). That this is a false dilemma should be obvious. One can certainly be opposed to terrorism and yet disagree with the how the US responds to it. For Bush to suggest that there are only two possible options is as clear an example of the false dilemma as one is likely to find.
As in the clips above, it is very common to combine a False Dilemma with a straw man. In setting up a false dilemma one makes one of the horns of that dilemma a straw man, thus pushing people to adopt the alternative horn. This is what we see in the above example. Bush is suggesting that if you do not support the US 100% then you are a hater of freedom and a terrorist. This again provides more rhetorical force for Bush's preferred option which is uncritical support for the US and its anti-terrorism policies.
Just to pile on a bit more, it is also worth mentioning that the US commitment to global freedom is fairly questionable as this piece from Glenn Greenwald highlights.