I'm afraid not - Tyk API Definitions are 1 target per configuration, with an optional override per API Version.
I'd invert your URL scheme though:
publicly api.company.com/prod/news --> origin newsapi.production.com/news
publicly api.company.com/staging/news--> origin newsapi.staging.com/news
publicly api.company.com/dev/news--> orign newsapi.dev.com/news
Then you can just set up three API Definitions in Tyk.
Alternatively, use the domain bindings:
publicly api.company.com/news --> origin newsapi.production.com/news
publicly api.staging.company.com/news--> origin newsapi.staging.com/news
publicly api.dev.company.com/news--> orign newsapi.dev.com/news