As we mentioned in the other thread AeroGear+Postgresql+Tomcat the aerogear quickstart example is based on JavaEE and so has some additional requirements that are not part of Tomcat. Specifically about the backend services (JAX-RS/REST).
The client side is straight HTML and so can be hosted nearly anywhere, but without the services to point to it won't do much :-)
The best approach will be to get JAX-RS, and CDI working on Tomcat (check their wiki's for instructions).
The client side piece is just straight HTML & JS pointing to RESTful endpoints. It does not really care what executes the RESTful endpoints, so as long as the services return the same as described here.