Quoting from the leaked document:

“The Home Office plans to make an offer to existing EU residents that they can remain in the UK in a ‘no-deal’ scenario, in effect unilaterally implementing the [immigration element of the] citizens’ rights agreement agreed with the EU in December 2017."

That word "unilaterally" is important, and represents a major concession on the part of the UK government, in that there's no stipulation for a symmetrical move by the EU re UK citizens living there.