Any chance to install npm without root access

According to this StackOverflow question, you must use socket.io's client-side code. Using websocket.org's client-side code is going to give you this error.

When possible, it is best to avoid compiling packages. In addition to often installing in non-standard locations, software that is compiled from source is much harder to keep up to date. Node.js provides a procedure to install from a repository - which includes npm and some other related components. The repository is kept up to date and is rarely more than a couple of days behind the source code. Moreover, instructions are available for Amazon Linux specifically:

sudo yum localinstall --nogpgcheck http://nodejs.tchol.org/repocfg/amzn1/nodejs-stable-release.noarch.rpm
sudo yum install nodejs-compat-symlinks npm.

npm should install to /usr/bin/npm which is a symlink to /usr/lib/nodejs/npm/bin/npm-cli.js. Of course, with some of the modifications made to your PATH, it is possible that npm may not be found. echo $PATH (as root) should resemble:

/usr/local/sbin:/sbin:/bin:/usr/sbin:/usr/bin:/opt/aws/bin:/root/bin

One of the common problems when previous installs with npm fail is a corrupted cache - clear your npm cache (npm cache clear) and see if you have any success. Of course, installing a package globally, needs to be done as root.