Despite the launch of a new dApp, there has been little engagement.

I haven't got round to trying it out yet. But I did today to give you some feedback.
Logging in with Keychain worked very well. I use it on the desktop. The first thing I noticed was the small game window. It's unusual for the desktop, but I think that's because you've developed the game more for mobile devices.

When I first look at the app after logging in, I don't really know what to do. I'm missing a ‘How to play’. Unfortunately, I'm also not an active player, so I'm not that familiar with apps like this. Maybe that's why. I've read the github.io page but still don't really know what to do.
I've managed to put together a deck with my three free cards and when I click on ‘Game’ the game seems to start. What exactly happens there is not yet clear to me. Anyway, I can see a countdown running. I think that's all I can do at the moment.

the community’s response has been largely passive.

If I want to be direct, I would say that this has nothing to do with the game. There have already been numerous discussions about the behaviour and appearance of new users... and the reading behaviour of the most users.
If I were to put it nicely, I'd say that I (and a few other users I know) are happy to help new users get started in the Steem if they contact me.
I/we recommend all new users to have a look around, ask in how-to posts and get to know each other. If the community doesn't know them, nobody can help them.
For example, I still don't know how to recognise the new users you've invited or where they hang out. Perhaps you can give me a tip?

But if the community also ignores the hundreds of new users joining through the game, how can STEEM expect to grow?

Even before your app, many new users appeared here every day. It is just not possible to know all of them, let alone take care of them. There were too many negative examples of people who used fake accounts to get help from others and then disappeared with the rewards. Or new users who expected double-digit votes as soon as they registered.
There are also positive examples and I am happy to support them. That also motivates me.

With this in mind, I'll now wait for the game countdown to expire and see what happens then...