take this with a grain of salt
I have not paid income taxes for most of my adult life, and for about 1/2 of that time, I have made a high 5 to low 6 figure income (mostly not from gambling). If you received a tax form when you cashed in that tournament, then the government has a record of that win. If you received no tax form (like every small-ish tournament I have cashed in live and been paid in casino chips), then the government has no record of your win.
After my business tanked about 10 years ago and I had a lot of personal issues pop up, I took a job for the Illinois Department of Revenue, and part of the hiring process was looking at my taxes for the past 3 years. Since I had not filed for the past 3 years, I had to go to the IRS and ask them for all of the tax records they had for me during that time so that I could file back taxes. They had nothing to give me and told me that it was my responsibility to keep all of my tax records for 7 years. During that 7 year period, I had multiple 1099 agreements with companies that were paying me for my work. I figured that is what I would have to pay taxes on in order to get this job and move forward. The IRS agent, at one point during a 45 minute long conversation, told me that I could either a) file all annual tax forms for the last 7 years with zero documentation and risk getting audited and having to figure out what to do after that or b) continue to not file.
I elected to file with zero documentation and zero income for 4 of the 7 years because I didn't have any information to complete the forms with. Nothing happened. I paid some tax on the info I did have so I could get that job, but no one batted an eye afterward.
I guess that my point is, even though there is a paper trail of your income (bank accounts, 1099 forms, etc), in order for the IRS to look at your income, there has to be something to trigger them to do so. The IRS can't audit someone that hasn't filed their income tax, it is almost like you don't exist to them. Sure, the government could find you pretty easily, but they aren't looking for you over one $13k payout. In the past 10 years, I have had 1099 forms issued to me over $150k and that didn't trigger anything either. $13k is an incredibly small transaction in the big scheme of things (but a great score for you!).
Now, keep in mind that I am a frigging loser and can't develop any credit and have to pay cash for everything and at any point it can all come tumbling down and I can get banged by the IRS on late penalties, interest on non-paid tax, etc. But, not paying my taxes has not led to anything catastrophic for about 20 years, so maybe you'll be fine?