Not a comprehensive answer but three main reasons:
First, the United States has not had an established religion and competing religious sects for hundreds of years. This means that religious denominations in the U.S. have had to compete to survive with little room for anything that makes them less relevant to their members. In contrast, the vast majority of countries either have an established or dominant religion that received state protection for most of its history in the country, or still does have an established or predominant religion. So, in other countries there hasn't been the same need to compete which has allowed these faiths to get away with doing things that prevent them from maximally engaging their members.
Second, in direct reaction to Communist atheism, the United States during the Cold War also adopted various measures (putting "under God" in the pledge of allegiance, putting "In God We Trust" on currency, posting Ten Commandments monuments) in what courts call "ceremonial deism" in an effort to boost the link between an American identity with a sense of being religious in a way that seemed inclusive at the time when almost everyone in the U.S. was Jewish or Christian and most atheists (there were few) were in the closet for their own safety given the prevailing environment.
Third, and closely related to the first point, is the empirically well established reality that religious institutions thrive when they protect a threatened culture, while they wilt when they are tightly aligned in beliefs with a secure, establishment culture that does not need religious institution protection.
For example, Ireland is one of the most religious countries in Europe, in substantial part, because Catholicism provided a refuge for Irish culture in the face of Episcopalian and Presbyterian English and Scottish rulers for hundreds of years. Similarly, in most countries, the most vibrant churches are those with recent immigrants who preserve their homeland cultures at church from their new foreign homes.
Most of the denominations of Christianity in the U.S. were predominantly immigrant churches within the last two or three generations.
Notably, providing a somewhat clean example, within the Roman Catholic church, which has very large numbers of recent immigrants (mostly from Latin America) and very large numbers of members who have lived in the U.S. for many generations (mostly European in ancestry), the levels of participation and religious identity felt by non-immigrant parishioners is similar to that of mainline Protestant Christians, while the levels of participation and religious identity felt by immigrant parishioners is much higher (and also much higher than the populations from their homelands from which they migrated).
Historically black churches are protecting and preserving a haven of African-American culture from majority American culture.
Most Evangelical Christians in the U.S. perceive themselves to be members of a minority culture and at the national level and with respect to economic elites this is true. So, a far larger share of Americans belong to threatened cultures which their religious involvement helps to preserve.
Other High End Outliers
One of the major upward outliers, Malaysia, is like the U.S., multicultural and has multiple significant religions, and like the U.S. has a substantial immigrant population in recent historical memory (the Chinese). These factors contribute to the preservation of a threatened culture aspect.
Indonesia is predominantly Muslim but split between a very conservative and a very liberal way of living that faith that the central government was trying to suppress until quite recently.
Turkey is also predominantly Muslim but has similar tensions between a Sunni Majority and a Shiite Kurdish minority, and also between adherents of a relatively secular public life instituted by Atatruk as part of the concept of the nation, and those who want to live a more openly Islamic life.
Lebanon likewise has three main religious factions (Muslims, Christians and Druze) whose political and daily lives are deeply segregated and influences by their religious identity, leaving all three feeling insecure and making religious identity relevant in daily life.
Originally, all of Latin America had an established Roman Catholic church, but in recent times, a Protestant, predominantly Pentecostal religious minority has emerged and this minority is more vibrant in Brazil than in many other Latin American countries. This may help explain its high end outlier shift.
Low End Outliers
The low side outliers like China, Japan and South Korea are all extraordinarily homogeneous culturally, and in China and Vietnam, for example, the official state policy of the Communist Party is atheism, so acknowledging religion is important to you (even if true) would be a dangerous way to provide an answer to a stranger conducting a survey. It also makes it troublesome and dangerous to try to be religious unless you really, really care. Also, the notion of what it means for religion to be important in your life doesn't necessarily translate well from an East Asian religion context to a question that was created with a Abrahamic religion (i.e. Jewish, Christian or Muslim) model as its court reference point.
In Russia, Poland and Ukraine, there was likewise a history of official state atheism in the Communist era, and there are few religiously diverse non-Slavic immigrants, so again, religion was artificially dampened for a long time and also doesn't preserve a threatened culture even now.
Technical GDP Related Considerations Impacting The Other Data Points
The GPD per capita number used on the X axis of the chart may be a flawed indicator of the poverty measurement the study is trying to make.
In many African countries, GPD per capita is artificially low because a large share of all production takes place in the non-monetary subsistence farming and do it yourself home production sectors that aren't included very accurately in GDP totals and with adjustments for that, the entire curve would move up more steeply at low incomes and the data points would be more tightly clustered.
For data points in Indonesia and Jordan, in contrast, GDP per capita may overstate income relevant to the purpose of predicting how religious the general population is, because both economies receive lots of GDP in the form of oil and gas revenues, much of which are siphoned out of country by oil and gas production companies or in the case of Jordan, to investments and the royal family, in both cases putting a significant share of the GDP out of the rich of even the affluent native people in those countries.
