Hi Momo!
I, too, would love a dedicated app for the site! Unfortunately I don't believe this is possible anytime in the near future. The site was built and is maintained by a single person (Kim) who does everything by herself. The only help she gets is some moderation help and photo bundles that are submitted to the site by its members, all other functionalities are created and maintained by just her.
In order to build an app, it has to support two major platforms (iOS and Android) and be updated/maintained alongside the website itself. Line of Action is not her only project, there are several more, including a daytime job to go alongside everything. Mobile apps are requested for virtually all of her projects, and she is the sole developer on all of them. I'm sure it's evident at this point how daunting of a task it would be to make mobile apps for all of them and still work a daytime job and keep everything updated every time the website receives an update!
Her solution so far has been to make the website as mobile friendly and accessible as possible. In most cases, you can create a bookmark to the site that can be tapped from your device's homepage and opens in a borderless window, immitating a mobile app. Notifications are also supported in Chrome/Android devices at this stage for a smoother experience.
I know this is not the answer you hoped for, but I do hope it brings some insight to the situation and that the bookmark option is a workable solution in the meantime. :)