If the Seller is a private individual, they (probably) can require a CASH offer.
Institutional Sellers, (banks and service companies) probably wouldn't try to require that; there would be too much jeopardy.
We have seen Banks favor CASH for Investors, but not overtly.
If a CASH buyer offered $200,000, and a Financed Buyer offered $220,000; which one do you think the Bank would accept.
When all the dust settles; everyone will have their money.
The LISTING does not specify CASH.
That looks like a lot of home for $129!
What does your Realtor say?