This is a challenging question to answer, as it raises questions of "what is capitalism?", and "what actually drives changes in life expectancy anyway?"

What is capitalism?

The term "capitalism" was first used in the 19th century, as a label for the existing economic system in the UK and other similar countries. Adam Smith, often known as "the father of capitalism", never actually used the term himself. In his 1776 book The Wealth of Nations, he talked about 'liberty' or 'natural liberty' and 'justice'. Often Smith criticised policies of his time that some future Marxists would describe as essential to capitalism (e.g. Lenin). For a couple of examples, Smith opposed European imperialism and also was stoutly critical of businesses (merchants, in his terminology) lobbying governments for subsidies and laws favouring special interests at the expense of the general public. Smith was actually very skeptical of comprehensive systems:

The man of system, on the contrary, is apt to be very wise in his own conceit; and is often so enamoured with the supposed beauty of his own ideal plan of government, that he cannot suffer the smallest deviation from any part of it. He goes on to establish it completely and in all its parts, without any regard either to the great interests, or to the strong prejudices which may oppose it. He seems to imagine that he can arrange the different members of a great society with as much ease as the hand arranges the different pieces upon a chess–board. He does not consider that the pieces upon the chess–board have no other principle of motion besides that which the hand impresses upon them; but that, in the great chess–board of human society, every single piece has a principle of motion of its own, altogether different from that which the legislature might chuse to impress upon it. [Theory of Moral Sentiments (1759)]

The 19th century, when the word "capitalism" was coined, decades after Adam Smith, was a time when historians and economists talked about "feudualism" as a distinct system of economic organsiation that had covered much of Europe in medieval times (Adam Smith did talk about feudualism). Karl Marx used the term "feudalism" extensively, and contrasted it with capitalism, viewing the two as having very different modes of production. Marx expected Communism to have a different mode again. Marx's intellectual influence has been huge, and many writings in the 20th century and even now draw on his conception of a distinct stage of capitalism.

However modern historiography, drawing on research carried out since the 1950s, has a very different view now of the economic organisation in medieval Europe. Generally, a lot more complex one that emphases variation between different places and the same places at different times. In the case of England, the medieval economy is now regarded as highly market-based and accounts of the Industrial Revolution talk more about a gradual change. To quote the economic historian Gregory Clark:

The more we learn about medieval England, the more careful and reflective the scholarship gets, the more prosaic does medieval economic life seem. The story of the medieval economy in some ways seems to be that there is no story. Back in the bad old days, when the scholarship was less careful, the medieval economy was mysterious and exciting. Marxists, neo-Malthusians, Chayanovians, and other exotics debated vigorously their pet theories of a pre-capitalist economic world in a wild speculative romp. But little by little, as the archives have been systematically explored, and the hypotheses subject to more rigorous examination, medieval economic historians have been retreating from their exotic Eden back to a mundane world alarmingly like our own.

And it's not just medieval Europe. Economic historians appear to have spent the last few decades engaged in a contest to see who can find the most features of modern financial markets back in Ancient Rome. Nor is it just Europe, economic historians find markets in pre-modern China, and just about everywhere else they have looked (see for example this book review on pre-colonial West Africa).

The result of all this research is that we now don't have any agreement of when capitalism came about, nor of what makes it distinctive. 

Take the UK in the 19th century. It started the century a very limited democracy (an estimated about 1 in 7 men were eligible to vote) and an imperial power, with various government economic interventions, including restrictions on international trade, it tolerated slavery abroad and boys being forced into the incredibly dangerous job of chimney sweeps at home, but with private property, poor laws providing income support for the poorest, and in Scotland a system of schools open to even the poorest. The UK ended the 19th century with a much wider male suffrage (60% of men), fervently anti-slavery, a much narrower poor support system, a primary education system for both boys and girls, free trade, but still an imperial power. Was the UK more or less capitalist in 1900 than in 1800? How about in 1950, where there was universal adult suffrage, the NHS had started, and there was rationing and capital controls, but the empire was declining? 

And there's nothing extraordinary about the complexity and variety of UK policies either. Even Hong Kong, famously libertarian under British control post WWII saw extensive government ownership of land. 

This can be contrasted with communism, where there are a number of countries where the leaders explicitly announced that they were socialist, and we can read their articles and speeches and follow the legal reforms they made seeking to achieve their ideals, and their setbacks. Not that there isn't debate about whether a country that called itself "socialist" or "communist" actually was.

In summary, there's no clear definition of capitalism that allows people to objectively distinguish capitalist countries from others. What's more, countries commonly called 'capitalist' exhibit significant variation in policies both at one point in time and across time, so if we see a country committing an atrocity it's hard to know what to attribute this to. So any answer to this sort of question tends to depend on the analyst's biases about what is distinctive about the countries they call capitalist and what causes atrocities, or improvements.

What is behind improvements in life expectancy?

For example, two countries generally thought of capitalist, the Netherlands and England were the first countries in recorded history to see the disappearance of peacetime famines, with the last peacetime famine being in the Netherlands in the 1590s, and in England in the 1620s. But this seems to be driven by a combination of broad technological changes and effective judicial systems, not any one factor like the enclosures. I wrote a comment about the start of the end of famine and the factors behind it 2 months ago for one of the floating features, if you are interested in learning more.

And, while Western countries were the first to see sustained rises in life expectancy from the mid 19th century, from the 1920s this spread to the rest of the world, including avowedly communist countries. But this transformation plausibly depends at least on part on technology developed in Western countries, but how much of that is due to market economies and how much to an expanding education system? Or some third factor, there's no requirement that what is important in economic development be easily identifiable, let alone measurable.

tl;dr post WWII economic history and economic histography have made this question unanswerable in an objective way.