He's playing word games, taking a specific meaning of amnesty and attempting to qualify it with short-term acquisition of citizenship:

First, "allowing people to stay here", means not enforcing immigration law for people who are breaking it.

"We’re not looking at citizenship, we’re not looking at amnesty"

Of course this is an amnesty and of course it will lead to citizenship.

am-nes-ty, n. an official pardon for people who have been convicted of political offenses.
par-don, n. the action of forgiving or being forgiven for an error or offense.

Whether it includes citizenship or not, it is amnesty. But it will eventually lead to citizenship.

Then he plays the emotional and faux corruption of blood arguments:

“We’re talking about taking care of people, people that were brought here, people that have done a good job and were not brought here of their own volition,” he said, referring to illegal immigrants brought to the United States as children."

This is wrong. Foreign nationals illegally entered this country with their foreign national children and began occupying it (necessarily requiring the commission of other crimes) while Democrats pushed the DREAM Act. But they failed to pass it in 2001, 2006 (mccain-kennedy), 2007, 2008, 2009, 2010, and 2011, so Obama overruled We, the People, and did it by executive memo with Napolitano in 2012 anyway. Then he doubled down and did DAPA to legalize the illegal alien parents.

We're talking about a lot of people who rushed into our country on the promise of amnesty, many arriving AFTER the commission of an unconstitutional act by King Barry Obama, and who have taken money and opportunities from American citizens, particularly our most vulnerable young people, siphoned money from our economy in remittances, created housing and infrastructure pressures, and committed a variety of crimes. And this when it isn't a straight-up case of fraud. How do you prove their stories?

Here's the pledge:

5. Immediately terminate President Obama’s two illegal executive amnesties. All immigration laws will be enforced - we will triple the number of ICE agents. Anyone who enters the U.S. illegally is subject to deportation. That is what it means to have laws and to have a country.

Trump is lost.