If you're not clear why this message is so cold -
Biden (and/or the staffer who composed this) is using a technique called "damning with faint praise," which is the rhetorical equivalent of "if you can't say something nice, don't say anything at all." Nothing he says is untrue, he just ... doesn't say much.
"I'll never forget the first time I met Dr. Kissinger..." A statement like this would normally be followed by a personal anecdote of some kind. But here it just stands alone.
"Throughout our careers, we often disagreed....." One would expect a but to follow this part, some way of softening such a statement by complimenting Kissinger. There isn't one.
"...his fierce intellect and profound strategic focus..." These are the nicest things the statement says about Kissinger, and the second one is a bit backhanded - "strategic focus" could be restated as "ruthlessness" or "knack for scheming" if they were willing to be rude.
"...he continued to offer his views..." This could be restated more positively if Biden meant it to be positive - "contribute his insights" or "share his wisdom." By using the very neutral "offer his views," the statement implies that's neutral is the best they could do.
"...and all those who loved him." This final sentence is brief and direct, and again, the absolute minimum Biden could say to be polite. It also delicately implies that the Bidens are not among those who loved him.
The whole thing avoids mentioning Kissinger's legacy, or even his actual government role. It's barely more than a form letter, and for someone so historically consequential as Kissinger, that implies Biden couldn't say more without being openly rude.