It's not clear to me what you need help with. Just our opinions of how likely it is the other buyer will be able to perform and remove the contingency or ???

I am a Realtor and in my area it is recommended to go ahead and make the offer to become a backup with the primary contract has a 72 hour kick-out clause, which is what you described in your situation. The reasoning is exactly as you pointed out. There are some buyers that have the capacity to close without selling their home first, but most need to sell their home or prefer to sell their home prior to taking on another mortgage.

Your offer, if acceptable to the seller, will motivate the primary buyer to either waive his contingency (if he can) or cancel the contract if he can't. Naturally, your offer shouldn't have a similar contingency or it wouldn't make any sense for the seller to swap out contracts without a benefit to the seller. I have sold several homes that were in back up position when the primary buyer couldn't perform. It is infinitely easier for the backup buyer when the kick-out clause is already in the primary contract. Good luck.

You will know in 72 hours whether the buyer with the contingency clause has decided to take the house or not.

I did this last year. I sold a small farm and suddenly needed to buy my next house. Inventory was low and my Realtor suggested we look at a house that already had a contract on it. The other places we looked at weren't acceptable, and it didn't hurt to look. As soon as I saw the house, I knew I could live in it happily for many years.

So we put in a contract, only contingent on the close of my farm, negotiated a little on price, and the contract was accepted. Then the dreaded waiting. Turns out the other buyer hadn't even put their house on the market yet, so they had to back out.

I got the house and am sooo glad, it was all meant to be! Good luck! You just never know what will happen until you at least try!