The answer depends on which server-side facilities of Errai your app is using. Here's a quick run-down of the major Errai features and what server-side requirements they have:
Errai Bus: Any Servlet 2.x container (or 3.0 for async dispatch)
Errai CDI container (without distributed events): no server dependency
Errai CDI distributed events: Weld >= 1.1.5 and < 2.0 (presently a hard requirement on Weld, not other CDI implementations)
Errai Cordova wrappers: no server dependency
Errai Data Binding: no server dependency
Errai IOC container: no server dependency
Errai JAX-RS in Jackson compatibility mode: no server dependency
Errai JAX-RS with Errai Marshalling: any JAX-RS implementation plus errai-jaxrs-provider
Errai JPA: no server dependency
Errai JPA data sync: any JPA 2.0 or 2.1 implementation
Errai Navigation: no server dependency
Errai Validation: no server dependency
Errai UI Templates: no server dependency
If you constrain yourself to the "no server dependency" features, you can even deploy on Apache HTTP, nginx, or any other non-Java webserver.
On a Java-based server where you can't deploy Weld 1.1.x, you can expect everything except distributed CDI events to work.
On a Java-based server that includes Weld 1.1.x, or one where you can deploy it with your .war (including Tomcat and Jetty), you can expect all of Errai to work.
Our demos whose poms include tomcat and jetty profiles should produce working apps for those servers when you mvn clean package -P[tomcat|jetty]. The main difference between these profiles and the jboss7 profile are that they include a lot more jars in the app (all the stuff you get for free in an EE container). Some of them (for example, jetty-env.xml in errai-cdi-demo-tagcloud) also provide static JNDI configuration for Weld in Jetty. You could use one of these demos as a starting point for your app.
We chose to leave the profiles out of our new errai-tutorial demo in an effort to simplify the pom and keep the number of possible branches in the tutorial to a minimum. We're trying to make the getting started experience as linear as possible.
Hope that helps!
As far I understand the key is to configure Weld with container, the rest is up to Errai modules I'm currently using. Thank you for your wide explanation.