My OS is Windows XP SP3, and when I tried running the installer for Vivaldi (TP2), it crashed. Does anyone have any idea why this would be the case?
No idea why it crashes. I don't know either whether Vivaldi is compatible with WinXP, but you could try to unpack the installer (using a packer like 7-zip or similar). It yields a file named "vivaldi.7p". Unpack it too. Move the resulting folder to a convenient location and start "vivaldi.exe".
…And probably unrelated to the installer crashing, but I'd definitely recommend starting with the most recent Developer snapshot.
Vivaldi is developing rapidly and there have been numerous bug fixes and feature improvements since TP2. Developer releases have generally been as stable, if not more stable, than TP2.
Follow the Team Blog for weekly updates (usually on Mondays) and occasional mid-week updates.
I finally extracted the files (Snapshot version) using Universal Extractor. When I tried starting Vivaldi.exe, it crashed, too, just like the installer did. I'm thinking it may be because of my old system. Does anyone know what the system requirements are for Vivaldi? Is there any way to find out what's causing the crash?
I haven't seen a list of minimum requirements, bit I've seen at least a few reports of Vivaldi working on WinXPsp3.
However, there may be a problem with chromium-based browsers on older CPUs without SSE2 support – see this thread.
Do other chromium-based browsers run on your machine? (Google Chrome, Opera 15+).
It might help if you could post a full description of your system specs and maybe specifically check whether the CPU has SSE2 support (introduced by Intel on Pentium 4 CPUs in 2001 per Wikipedia).