The price cap on Russian gas effectively sets a maximum price that those enforcing the cap will pay. This means that Russia can't sell at full price because even those not enforcing the cap aren't willing to pay full price for it (why should they, when Russia's choices of customers are severely limited?). It's an artificially induced market pressure to keep prices down.
Does it stop Russian gas from flowing? No, but that's not the point; the point is to reduce Russia's profits from the gas. The world still gets all their gas, but Russia gets far less money for it.
Does it mean that Russian gas doesn't make it to Europe anymore? Nope. In fact, "Russian" gas probably makes up a big chunk of imports to price cap countries. But since Russia can't charge full price for its gas, the profits go to the middlemen, who raise prices to the actual market rate and pocket the difference while shipping to whoever (including price cap countries, because once it's owned by the middleman it's no longer "Russian" gas, but regular market rate gas).
So what is this "independence from Russian gas" all about then? It's about not being directly dependent upon Russia for providing the gas (i.e. Russia can't threaten to turn off the taps if Europe doesn't toe the line). The only thing Russia could do now is stop supplying gas to everyone, which would be even worse than the reduced profits they're suffering already.