Mobile device compatibility for wordpress arcade website

Hello All!

First of all I am not sure that this is the right category to post the following question. So please correct me if I am wrong… here is the question:
I want to create a gaming arcade website using a plugin like the one available at http://myarcadeplugin.com/

My concern is that if I do that, since these games are flash based, the modern smartphone devices will not support it. Am I correct? If yes, then what is the workaround for this since these devices support html5 and not the traditional flash5 since, I guess, it conflicts with the idea of apps & its ecosystem that these smartphone platforms have for themselves.

Pls. note that I have contacted the website & am awaiting a reply, but I guess the WP community might throw its own light into the matter. Has anyone faced the issue I am having and what is the resolution that worked for you?

Thanks in advance 🙂