Never be daunted by job-posting lingo. Half the purpose of that lingo is to rule out people who are uncomfortable with the terms. Learn a popular web development framework and start building. Today. With or without a job.

Then parlay that into your interview process. Do NOT get hung up on "gee, I have no idea how to scale to ~1 million users." Almost nobody entering web dev for the first time knows how to do this. Many who've been doing web-related work for years don't know how to do this. Scalability is just one aspect of web dev and for a majority of projects (corporate IT projects with 1 - 100 users) it's a complete non-issue. Nevertheless, they might still say "experience building scalable web applications". Do NOT let this stop you from interviewing.

You have one huge advantage while seeking a job in web dev as opposed to the desktop world: your work is immediately visible to anybody in the world. Every website you build is a portfolio piece. And if you can discuss these in the interview, and communicate above all your enthusiasm for the work, you'll get the job. Somewhere.

Good luck!