Can I use this with a browser that's not Chrome-based?
No.
Well that's disappointing. I mean, it's license is pretty restrictive, so I probably wasn't gonna get too close to it, but the hardline of no browsers other than chrome is kinda disappointing. Back to the drawingboard.
The license mentions that all previous licenses are revoked. Is that even possible to enforce? If I had forked a prior version with a different license, couldn’t I just use that instead?
(not a lawyer) It depends. Some jurisdictions give copyright holders more power than you might expect, if you used the software under the new license you might implicitly agree to such a term, and some licenses explicitly give the copyright holder revocation privileges.
In a lot of places most open source licenses can't be revoked on a whim unless the person using them violated the terms. It's pretty common for communities to fork an old version when the parent project does something wonky with the license.