x2 should not slow that card at all, especially not in that system.
The primary need for high PCIe bandwidth is for when your graphics card runs out of memory so has to substitute system memory instead. Think of it like when you run out of system memory so it starts swapping to hard disk instead, which is so much slower it makes everything pause. In your case the system memory is so slow that everything would freeze up anyway, were it ever used to replace video memory. So both x8 and x2 would effectively perform the same--both are unusable and the moral is never run out of memory.
The main problem with that system is the processor is only as fast per clock as a Pentium 4 for single-threaded workloads. So in 2017 you are using the equivalent of four Pentium 4 2.5GHz from 2002 (although using only 6w instead of 244w). A 2.53GHz Core 2 from 2008 is 3x faster per core in Java, and today's 2.5GHz Kaby Lake is 7.5x faster.
So while the video card is no faster than today's fastest integrated graphics, the CPU is like something from 15 years ago. Without hardware acceleration assist from the video card, web browsing would be terrible. BTW that Pentium 4 likely was used with AGP 4x, which has about the same bandwidth as PCIe 2.0 x2, so x2 is even well matched to your processor.
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