Because you did not have a contract guaranteeing you the right to a job with that employer, they were legally able to let you go for any reason, so long as that reason did not involve illegal discrimination against you----which it seemingly did not. Even though you may have been defending yourself, the employer had the legal right to terminate you for cause---which would simply be fighting on the job site.
Unless you could somehow prove that you did not violate any rule of the employer, which would presumably require that you prove that you engaged only in self-defense which was absolutely necessary to prevent bodily injury to yourself----which is going to be a very difficult thing to prove without at least having several witnesses prepared to testify on your behalf, then you are not going to be able to obtain unemployment benefits.
If you want to tilt at this windmill with unemployment I must strongly urge you to hire a local employment law attorney because this may well end up in the court system---as I suspect you will lose at all levels of the unemployment appeals system. I guess what I am telling you is that your chances of success are slim, and if it were me, I would not waste the time and money fighting over the benefits.
I understand that you may be disappointed by the Answer you received, as it was not particularly favorable to your situation. Had I been able to provide an Answer which might have given you a successful legal outcome, it would have been my pleasure to do so.
If you have additional questions, you may of course reply back to me and I will be happy to continue to assist you further until your questions have been answered to your satisfaction.
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Thank you in advance. I wish you the best in your future,