You are correct to have concerns about safety with downloads. There are many sites now that bundle unwanted junk or even malware with the app you want.

I assume you are running Windows, so the best place to get SS is from Microsoft, here

https://www.microsoft.com/en-au/store/p/simple-spider-solitaire/9wzdncrdkrdt

Follow the links, 'Get the game' then 'Install' and subsequent instructions and you should have a desktop icon.
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