You can get a VPN service that has international routes and subscribe to international versions of services like NBA League Pass and NFL Game Pass. The major sports leagues negotiate deals with U.S. TV providers that prevent the leagues from streaming directly to customers without a cable/satellite subscription, but they are able to sell streaming subscriptions to international customers.
I may or may not do this with the NBA and it works well enough. For the NFL, I'm generally happy with the games that I can pick up with my HD antenna on my TV, so I haven't tried their service.
You have to pay a few bucks a month for the VPN, but I like having a VPN service available anyway, so it's not a big concern for me and you're still saving substantial money over cable.
The people who start a company that bundles VPN + international services into a simple "Chromecast" device will be billionaires... or sued because of some legal issue.
My Chromecast works fine* with my VPN, I use it to watch Netflix in Greece.
* With a router that can intercept DNS requests.