In short because economy is not a zero-sum game and because economic production does not need to decline but can grow over time.
First of all, forget about money. Money in economics is just extra tool that solves issue of double coincidence of wants, allows you to store value over time and to do accounting. In fact, traditionally money consisted of commodities such as stone, or precious metals or even products, coffee, cigarettes or even alcohol etc at some point in time and place served as money.
As a non-economist this might come as a surprise to you but most microeconomic models do not even have money in them. Money can play an important role in macroeconomic perspective because in the short-run it can affect the real economy, but from micro perspective and even long-term macro perspective money is neutral and not important.
Next, as you pointed out a world's economy, taken as whole, is a closed system but that does not mean people should get poorer over time. This is not an equivalent of thermodynamically closed system where entropy has to dissipate energy overt time. A closed economy can be described as:
$$Y = C + I + G$$
which says that output/income (they are economically equivalent) $Y$ has to be equal to consumption $C$, investment $I$ and government spending $G$. In turn, $Y$ is a result of production. A common specification for production process would be to use Cobb-Douglas production function, so I will do that here as well, although in principle there could be multiple functional forms that production process could have. Moreover, for simplicity I will restrict myself to two factors of production (labor and capital) even though in principle you could put into Cobb-Douglas also human capital (education), land and other factors, but I omit them for sake of brevity. Given these assumptions the production process would be given by:
$$Y = A K^{\alpha} L^{\beta}$$
where $A$ is the available technology (broadly defined - in economics better production strategies count as a technology as opposed to just 'gadgets' such as PC), $K$ is the stock of capital and $L$ is the stock of labor. Alpha and beta are parameters of the production function that determine other characteristics of production such as what sort of economies of scale production exhibits (e.g. increasing, decreasing or constant).
Thus, we can say that the consumption, investment and government spending is equal to this production process:
$$ A K^{\alpha} L^{\beta} = Y = C + I + G$$
So as long as technology $A$ or capital $K$ or labor grows, output $Y$ will grow as well and even completely closed of economy can consume more, invest more or have more government spending.
Furthermore, what we really care about is usually output/income (in economics output and income are equivalent and interchangeable) per head. So if we for simplicity assume constant returns to scale ($\beta = 1-\alpha; 0 < \alpha < 1$) we can divide the last expression by $L$ to get whole expression per capita as:
$$A \left(\frac{K}{L}\right)^{\alpha} = \frac{Y}{L} = \frac{C}{L} + \frac{I}{L} + \frac{G}{L} $$
Here, if we keep the population growth constant then we can see that per capita incomes/output and consequently per capita consumption, investment and government spending will grow when our capital stock and technology stock grows. You get growth in capital stock from investment (investment is part of production that is not consumed but saved for future, possibly for further production), and growth in technology from human ingenuity or also depending on which economic growth theory you buy to also investment.
In addition, all the above is up till now just manipulation of definitional expressions. We could further continue by adding on some growth theory which could yield further insights. For example, the most popular growth model presently is the Solow-Swan growth model where it can be shown that what really matters is growth in $A$ because increase in investment and capital stock can only increase level of output not growth. If you buy into endogenous growth theories investment can even increase the growth rate further beyond that (you can read more on this in Barro & Sala-i-Martin: Economic Growth 2nd ed).
In order for people to get poorer over time (in per capita terms) an economy would have to experience either destruction of technology (for example ancient Romans, Greeks, Carthaginians etc had plumbing but this knowledge was lost in many parts of World - but not all - during dark ages, or another example would be concrete) or by destruction of capital (e.g. war, violence, natural disasters etc. but also just wear and tear i.e. depreciation). Empirically, and let me add thankfully, people historically turned out to be better at producing new technologies and adding new capital through investment, than at destroying either of them.
Consequently, to sum up people do not get poorer over time and in fact get richer because of growth in economic production (which in turn determines people's income), and economic growth occurs primarily thanks to growth in technology and investment. In fact note because the economic growth is to large extent driven by technology, it is possible for economic production to grow indefinitely (assuming technology has no limit - e.g. in real life it is possible you can't get at an end of technology tree like in some strategy game as it might have no end). In addition, more rich models would also include other important factors such as human capital (education) but the explanation above would not conceptually change (education macroeconomically functions in same way as capital - hence why economists call it human capital).