implied in the site name -- skip the games -- and just never go so don't have to worry about such things.

I don't do STG.  I do run NordVPN.  It allows to select the country you want the VPN to be in.  Could it be country specific (IP's blocking certain countries?)

I use TOR (free VPN and a secure browser combo). Sometimes STG gets through, sometimes it doesn't. Same thing with Tryst: sometimes Tryst gets through, sometimes not. And so on for several other sites (even Google ["Too many inquiries from your IP address. We think you're a bot." errors. And Youtube is sometimes blocked. I rarely click on Youtube links because it's a waste of time -- sorry, Robertini, I rarely click on your many Youtube links.]  
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I hope I understand this correctly. TOR uses onion routing. Me--ConnectionServer1--Conn2--C3--C4--destination (e.g., STG). Every few minutes, TOR changes the Connection Links: Me-C12-C32-C3-C17-destination (e.g., STG).
STG only sees the last Connection Server. If STG doesn't like C4 or C17 for some reason, it blocks sending the info back through the chain STG--C4--C3--C2--C1--Me or sends an error message. Sometimes, the random connecting server is fine with STG's server and I DO get the page content.  
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Sometimes, it is TOR and the TOR Browser that detect unsafe code and block the webpage from getting through.
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Like the OP, I am not going to change TOR Browser or other settings to weaken my security just to see an ad or a Youtube.  
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I have repeatedly recommended to Providers with their own websites that they ask their webmasters to test the site (try to access the site) using TOR (more than once). If there is offending code that TOR or other VPNs don't like, modify the code!

It's not really exclusive to stg, many sites do this to a different degree.  

The best advice is to cycle through your available ips and perhaps find one that isn't blacklisted. If you use a major, well known vpn and stg bl is extensive, your chances aren't good. If you are an advanced user, try to find some utr vpn/proxy. Don't use it for anything but https traffic so even if it's security is iffy, you will be encrypted and can work with sites you want.