This line is perhaps the most important:
After winning they said they want me to spend it in store before a certain date and record my process and how it changed my life.
It's a PR stunt. They want to use the Winner of the competition to go on Camera and say nice things.
To answer your question directly:
'Can I just get the money' - most likely, No.
The reason is this - it might be a '$10,000' Gift card, but in terms of cost to the company (depending on the markup) - it's in reality only going to be about $5,000 or less.
You asking for the cash value is going to cost the company more than they wanted to pay.
In addition, the company is clearly wanting this exercise to pay-off in terms of a marketing campaign or internal promo video. They could just write a script and have actors do it, but they want an authentic experience - in the hopes that will connect with the audience more.
To answer your other question - Are you going to get Fired? Probably not either (caveat here about At-Will states if you are in the US).
First question though - you say there's nothing in the store that you need. I'm presuming that you can't say the store for fear of revealing who you are etc. So let's do a hypothetical - let's say the Store is 'Bobs Firearms and bullets' and you are a principled Pacifist who refuses to even touch a weapon.
Starting from the most extreme position - where you have a fundamental moral objection to the product being sold - I'd sit down with the company and discuss this aspect with them. Bob might have a sister company that is Bobs Mowers and Gardening - which might be more to your taste (as I'm assuming a prize of that magnitude isn't being done by a small business). There might be some wiggle room or there might be other institutions in the chain that you might be more interested in that could come to some arrangement.
Keeping with our initial hypothetical, let's say that you don't have a moral/philosophical issue with the product, let's just say you don't like to shoot. In which case, how I'd handle this:
I'd do my research as to which products at the store sell second-hand for the highest percentage of the original sale price, Buy a bunch of those till the card is maxed out, Come up with some half-truth spiel about how it changed your life - then flog them all on Ebay/Trademe/Amazon/Wherever as soon as you've fulfilled your contractual obligation. It might take a bit longer, it's not the $10K hard cash in your hand, but it's still better than nothing.
Next option (keeping the Gun theme) - you've got yourself a sufficiently stocked Gun Safe with a .22, a Shotgun and your hunting rifle and 'that's all I'll ever need' - in which case my suggestion would be to simply splurge. There's stores that I go into that I might have very little interest in spending my own money on, but if you give me $10K of your money and tell me I have to spend it there - I'm sure I can find things to buy. It might be something that you envision yourself only using once or twice - but now you own it and you don't have to hire it or rent it and you can lend it to friends etc.
Then as above - come up with some life-changing message 'Since buying the splurge-9000, it's really brought my local community together - we've had neighbours come and borrow it, seeing them be able to beautify their little spaces has been more reward than any monetary gain' or some other sappy spiel.
At the end of the day, think of it from the Companies PoV - what is it they want?
They want marketing material - whether it's internal to say 'Wow, aren't we such an amazing employer that gave this person the chance to change their life direction! Work for us and you too could be the next person!'
"Buy our product because we don't treat all our workers like Slaves! See we even had a competition where one out of our 5,000 strong work force was able to do this with our generous giftcard!"
Talk to them and find a way to satisfy what they want to achieve, and you'll probably find that they are okay with just about anything else.