The fact that it was the company's decision to eliminate your job has a whole lot of benefit to you. Their choice - and you have a right to make a living. I doubt seriously if they can make this non-compete stand up in court. Of course we don't know the complete details. So that disables any of us from giving accurate info back to you.
It is not wise to sign a non-compete without reading it well. However vague non-competes often work against the companies that wish to enforce it, so many signing one that is vague and incorrect is a better option than making sure it specifically spells out accurate details.
I used to work for an employer who would electronically send out the non-competes to sign every year (huge corporation). The last one that was sent to me, I objected to because it included statements that required not only me, but that my immediate family would be bound to it. Since I have no legal right to prevent my grown children from working anywhere they wish, I did not wish to sign this. There was no one to call and speak to. The website allowed me click and agree to it but not to reject it. I replied to the entity that sent it, but received no response. A month later, reminding me I had yet to acknowledge it. It stated it was a condition of employment. I went to HR who suggested "just sign it, it's not a big deal", but I refused. A month later, another email. I forwarded it to HR and my boss, again stating my objections. The HR manager thought I was being silly, my boss agreed with me. So we waited it out and ignored subsequent emails. Eventfully the emails stopped after six months. I never did lose my job (quit a few years after that). They asked me to sign a non-compete when I resigned (different document at this time and more reasonable). I refused because there was no benefit to me (no severance, no benefit in jeopardy, etc.) and they couldn't stop me from leaving - it was my choice.

