The Domino Theory always related to the geostrategic concern that if one state fell to Communism (e.g. China in 1949) then surrounding states would follow. The US had never been especially friendly with the Soviets – having only joined forces with them in WWII to oppose Hitler – and after the war both states emerged very powerful but with converging interests. Soviet communism flew in the face of deep-seated American values (i.e. capitalism, free enterprise, etc.) and it seemed as though this may not stay within the borders of the USSR. The Cold War really began with warnings within the Truman administration that birthed the policy of ‘containment’ – particularly from Ambassador George Keenan – that the USSR would not be a peacetime ally since it sought to export its political ideology. The fact that the Soviets had occupied much of Eastern Europe in 1945 (albeit with Allied permission) gave legitimacy to these fears about Soviet hegemonic ambitions.

The fear was not (initially) rooted in direct security threats to the American mainland, but to US economic interests abroad. If Western Europe fell, the US would lose key economic and political allies. American trade would be compromised if more of its allies fell into the Soviet sphere. They had expended many resources over the course of WWII to protect such interests. Of course Truman and his cabinet also saw a threat to the American way of life and to the global capitalist system which nourished it. Their interests across the globe were perceived as threatened so long as the USSR’s own influence – seen as directly contrary to their own – grew. So despite the fact that Stalin’s policy of “Socialism in One Country” had existed since the twenties, the fear that American interests may be threatened by an unprecedented Soviet military capacity was prioritized.

The Domino Theory had many holes, particularly visible after Vietnam, but context is important. The US had just joined the rest of the world in major conflict that shook the global economic system for years. Thus it was not out of the question that one man’s political vision may usher in a repeat, especially when Stalin’s personality was considered.

SOURCES: Melvyn P. Leffler, David S. Painter. Origins of the Cold War: An International History. 2005. George Keenan. "Long Telegram." http://www2.gwu.edu/~nsarchiv/coldwar/documents/episode-1/kennan.htm.

EDIT: Sources added.

I would recommend reading George Kennan's "Long Telegram" and "X Article" as its my understanding that their publication is regarded as the watershed moment in a shift of US strategic thinking on Russian intentions and the US policy response.

In the Long Telegram, Kennan, who was deputy chief of mission in Moscow, characterized soviet foreign policy as follows:

"(a) Everything must be done to advance relative strength of USSR as factor in international society. Conversely, no opportunity must be missed to reduce strength and influence, collectively as well as individually, of capitalist powers. (b) Soviet efforts, and those of Russia’s friends abroad, must be directed toward deepening and exploiting of differences and conflicts between capitalist powers. If these eventually deepen into an "imperialist" war, this war must be turned into revolutionary upheavals within the various capitalist countries. (c) "Democratic-progressive" elements abroad are to be utilized to maximum to bring pressure to bear on capitalist governments along lines agreeable to Soviet interests. (d) Relentless battle must be waged against socialist and social-democratic leaders abroad."

He specifically believed that this policy was being carried out in the following countries and to the following ends: "(b) Wherever it is considered timely and promising, efforts will be made to advance official limits of Soviet power. For the moment, these efforts are restricted to certain neighboring points conceived of here as being of immediate strategic necessity, such as northern Iran, Turkey, possibly Bornholm. However, other points may at any time come into question, if and as concealed Soviet political power is extended to new areas. Thus a "friendly" Persian Government might be asked to grant Russia a port on Persian Gulf. Should Spain fall under Communist control, question of Soviet base at Gibraltar Strait might be activated. But such claims will appear on official level only when unofficial preparation is complete."

I think when you say that you can't see a direct threat to the US in all of this that he addresses that aspect of Soviet policy as well. They are in effect a rival, not an imminent threat like Hitler: " (1) Soviet power, unlike that of Hitlerite Germany, is neither schematic nor adventuristic. It does not work by fixed plans. It does not take unnecessary risks. Impervious to logic of reason, and it is highly sensitive to logic of force. For this reason it can easily withdraw--and usually does--when strong resistance is encountered at any point. Thus, if the adversary has sufficient force and makes clear his readiness to use it, he rarely has to do so. If situations are properly handled there need be no prestige-engaging showdowns."

He doesn't use the word "domino." In fact my understanding is that that comes later, after key setbacks in like China in 1949 (prompting the famous discussion over "Who lost China?") and the Korean War.

But in terms of outlining the Soviet threat and the appropriate American response that is, in effect, what he's describing is about to happen.