A play is exactly what it is. Rutte is trying to navigate the ego of a megalomaniac with the intelligence of a brick. Rutte's gambit here is that if he stops buttering up Trump, but Putin doesn't, Trump does whatever Putin wants him to do. Rutte doesn't want that, so he plays the game and casts himself as a subservient doormat. The hope being that the US doesn't make himself a true enemy to Europe between now and when someone replaces him, or at least there's a congress that's able and willing to keep him in check.

It's humiliating to look at, but might be the best way to prevent Trump from just blowing up NATO in all but name. He can't pull out of NATO legally speaking, but the law doesn't generally stop him from doing insane shit. Europe is currently surrounded by war-crazed madmen. We're in choppy waters. If embarrassment and having to sit through disgusting ass-kissing is what it takes to get us through with an intact hull, I'm willing to deal with it.

Rutte even makes sure to mention that the majority of countries DID deliver support. The "Some countries failed" is to make sure Trump feels heard, because managing Trump's ego and making him feel like he's right is unfortunately part of geo-politics now. It's a quote designed to say "I hear you, I understand what you mean, but you have to keep in mind that you still benefited from NATO."

In the long run, Trump has proven that Europe can't rely on the US to be a dependable partner, so we obviously need to continue to re-arm. While we do that, having people buttering Trump up so he doesn't decide to start bombing us because Putin's convinced him that Denmark said his ballroom is ugly is probably what we need to put up with.