You can think of "putting out" as "putting" in this sentence. It means that Russia has put some sort of a boundary around it. When it says "got itself in a blind", it means that Russia is in a way isolated from the rest. "Blind" can be thought of as Russia not being able to see the rest of the world.

Actually, I don't think "put out" is the best phrase to use in the sentence you provided but it is at least acceptable usage. "set out", "establish", "declared" would be better words or phrases to use. That said, the point of the sentence is that NATO established clear boundaries of action ("Red Lines") that it warned Putin must not be crossed. The "bind" that NATO has put itself in is that Putin can now do whatever he wants as long as he does not cross those boundaries because NATO has basically promised not to punish Putin as long as he does not cross the "red line". One way to understand this paragraph is to imagine a school that has a rule that states, if you are late to school more than once a week, you will be disciplined. In effect, this gives every student permission to be late to school once a week without being disciplined. Some students will "walk right up to the line" by being late to school exactly once every week but no more than once in any given week. Another real-life example can be found in the speech of U.S. Secretary of State Dean Acheson to the National Press Club on Jan. 12, 1950. In this speech, he declared that the U.S. and the United Nations would defend a "defensive perimeter" that ran from the Aleutians to Japan to the Ryukyu Islands and then to the Philippines. Some people have criticized him for not explicitly mentioning South Korea as part of this defensive perimeter and have alleged that this omission caused the People's Republic of China to conclude that the U.S. would not defend South Korea from an attack by the North Korean army. Whether or not this criticism is valid, the point is that Acheson laid out a "red line" defensive perimeter and it is claimed that the Chinese assumed they could walk up to the defensive perimeter with impunity. Tragically, the events of history proved that this was not true.

"Putting out" would mean "declaring" or "delineating". That is, NATO has decided which "lines" mustn't be crossed, and has made Russia aware of this decision. NATO's decision has actually limited and restricted what it can do - to be "in a bind" means you're in a tight or difficult situation. Think of ropes that bind your wrists and ankles.