I can't answer your question properly, in part because I am not BERI. I'll just share some of my thoughts that seems relevant for this question:
- I expect everything BERI supports and funds to always be justified in terms of x-risk. It will try to support all the parts of EA that are focused on x-risk, and not the rest. For example, their grant to EA Sweden is described as "Effective Altruism Sweden will support Markus Stoor’s project to coordinate two follow-up lunch-to-lunch meetings in Sweden for x-risk-focused individuals."
- I think it would be correct to classify it entirely as an x-risk org and not as an EA org. I don't think it does any EA-style analysis of what it should work on that is not captured under x-risk analysis, and I think that people working to do things like, say, fight factory farming, should never expect support from BERI (via the direct work BERI does).
- I think it will have indirect effects on other EA work. For example BERI supports FHI and this will give FHI a lot more freedom to take actions in the world, and FHI does some support of other areas of EA (e.g. Owen Cotton-Barratt advises the CEA, and probably that trades off against his management time on the RSP programme). I expect BERI does not count this in their calculations on whether to help out with some work, but I'm not confident.
I would call it an x-risk org and not an EA-aligned org in its work, though I expect its staff all care about EA more broadly.