Your "listen" directives are wrong. See this page: http://nginx.org/en/docs/http/server_names.html.
They should be
server {
listen 80;
server_name www.domain1.com;
root /var/www/domain1;
}
server {
listen 80;
server_name www.domain2.com;
root /var/www/domain2;
}
Note, I have only included the relevant lines. Everything else looked okay but I just deleted it for clarity. To test it you might want to try serving a text file from each server first before actually serving php. That's why I left the 'root' directive in there.