In a debt based fiat money system, it is a zero sum game, your saving comes from another people's debt, so your conclusion is correct

But in a debt free money system like bitcoin, it is totally possible that everyone are rich, since every BTC existed are not a kind of loan, the electricity, time and R&D cost of the mining equipment has all been paid and contains in each BTC, it is debt free and have value coined in, everyone can get BTC with their product/service without incur a debt somewhere else in the society

Ignore the USD exchange rate, that partly depends on the USD supply by FED, do not really represent the real value of BTC, market is discovering that value now

Yes, we can all get rich if we keep voluntarily assigning value to bitcoins in terms of goods and services we trade via Bitcoin network. If more and more people keep valuing their labor, fiat, or property in terms of bitcoins, the value of coins will keep rising. The opposite applies, too.