Okay first off, I'm not going to talk about islam in this answer. I don't have enough knowledge about it's history to be able to speak to the dynamics involved there, so I won't try. This will be focusing on the effects of christian missionaries from the early modern period on.
Second of all, I think it is important to acknowledge that many indigenous religions in Africa and the Americas are not dead. Many people in these regions still practice their ancestral religions to this day and there are efforts to preserve them. It cannot be denied that christian missionary efforts did a lot of damage to these traditions and cultures, a lot more than they did to hinduism, but in many cases they did not manage to destroy these religious practices entirely. Saying they're all dead arguably does the work of the missionaries for them.
But yes, christian missionary efforts were much more successful in Africa and the Americas than in India (and East Asia) at large. In my opinion this can be largely chalked up to several reasons, some on the side of the colonisers, and others on the side of the colonised.
We often think of European colonial regimes as being the same everywhere: a group of white Europeans come in, take the land and try to convert or genocide the locals and use their resources for their own profit. But this disguises the fact that the various colonial regimes were often quite different from each other, including in their religious policies. In Africa and especially the Americas, colonial governments were often very favourable to promoting conversions and giving christian churches certain degrees of power. The Spanish in Mexico very deliberately promoted the destruction of pagan cults and the conversion of the locals to christianity, seeing it as a continuation of their role as defenders of christianity during the reconquista. We've all heard, in recent years, about the residential schools in the USA and Canada which were designed to turn Indigenous children into "civilised" European christians by force, initiatives which were very much run with government approval and aid. And in Belgian Congo, missionaries were given wide leeway in spreading their faith, even when the government at home in Belgium adopted anticlerical measures at home, because they were seen as essential in civilising and controlling the area. But by contrast, the European trading companies active in India and South-east Asia were not interested in this. They were there just to make money, and christian missionaries going around and upsetting the local population and especially local rulers with their preaching did not fit into that. When the British government took over the rule of India from the EIC, they generally kept a similar stance, not outright preventing missionary work but not particularly encouraging it, not in the same way many other colonial regimes did in other areas. Christian missionaries in Africa and the Americas could therefore often count on government support for their initiatives, whereas in India they were more often individuals or (sometimes quite powerful) misionary organisations acting independently in the face of an indifferent government and often hostile population.
We also have to acknowledge the very simple fact that many cultures in North America and to a lesser extent Africa were victims of genocide, plain and simple. Many of the colonial regimes in these areas tried to erase certain cultures and their religious traditions from the face of the earth and open areas up for European/white settlement. Not in every case, and they certainly weren't always successful, but this did happen often. By contrast, while I'm sure a few British officials in private might have entertained such plans for India in the same way that some of us muse about how we should completely change our voting system over a few beers, and there were targeted small attempts at genocide against certain groups, they never tried to genocide the whole hindu population. That matters.
A third reason lies in the local religious context. Traditional religions in the Americas and Africa generally did not exist in an adversarial context. No missionaries were travelling from Hausaland to convert the kingdom of Kongo. The Pueblo culture didn't lead crusades into the Mississipi valley to destroy the idols on the mounds. That simply wasn't how these things worked. This is not to imply that these religious traditions were primitive or unsophisticated, or that there were never philosophical discussions going on. But there simply wasn't a tradition of trying to convert others, or prevent others from being converted. There was no such thing as conversion.
But christianity? Conversion is a core part of it's tradition. Christian scholars have been talking about how to best convert other people to their religion almost since its founding, and for almost just as long they have been putting this into practice. By the time the early modern period came, there were plenty of examples and expertise to draw on for evangelisation, and for the next centuries christian missionaries would get to do it on an unprecedented scale, giving them even more time to hone the practice.
If you'll forgive me a slightly simplified metaphor, it's like arranging a boxing match between two men, and one has been training since birth to box while the other hasn't. It doesn't really matter that the other guy is a great gymnast or cyclist, we know who's going to win that match.
This isn't true for India. There was a very old tradition of philosophical debates within hinduism. Moreover the religion had faced fundamental challenges from other new religions such as jainism, buddhism, islam and sikhism. And in the face of them hinduism had often reinvented and redeveloped itself to respond to these challenges and maintain its appeal and hold on its practicioners, such as during the Gupta empire. On top of this, hinduism was of course heavily entangled with the authority of community leaders from the brahmin caste, and they weren't excited to let people abandon the model which gave them a large part of their traditional authority. To put it simply, by the time christian missionaries arrived, hindus knew how to box and a lot of them were quite ready to do so.
When discussing these big institutional reasons, it can often obscure the actual people involved. Conversion movements are, ultimately, made up of individual people converting. And their individual stories and reasons for doing so have varied a lot. So when we think about this question, it shouldn't be thought of as a simple list of advantages and disadvantages in a battle between great abstract forces.
Why did these people convert? Because becoming a catholic might have been a way to keep their position of authority under the new rulers. Because if they became a christian, there was a greater chance that the Europeans would grant them at least some basic human rights. Because they found the missionary's preaching genuinely inspiring. Because the missionary's knowledge of mathematics and science impressed them and they could learn more about that like this. Because as a child, they were taken from their family to an "orphanage" and they didn't have much of a choice. Because if they just converted, the christians would give them a bowl of rice. Because there wasn't really much of a point in not doing so, when the Europeans had destroyed the traditional sanctuaries and either burnt all the ritual implements or carried them off to museums. Because it offered a way out of a traditional society which limited their options.
Why did people not convert? Because the christian preacher had made a fool of himself while preaching because he didn't know the language. Because the king had always taken care of them, and the king wasn't christian, so why should they. Because abandoning the traditional wisdom passed down by their ancestors was unthinkable. Because the christian answer to what happens to us after we die didn't make sense. Because the traditional ways have always worked, why change? Because these people came here, took our land and killed our family so why should we give them our souls as well? Because if they converted, they would have to deal with a rejection and loss of support from their family and community.
And a million other ways in both directions. These were all personal reasons, but the greater picture influenced the reasons and the behavior of these individuals, and in general it incentivised conversion in Africa and the Americas while not incentivising it as much in India.