I just googled gaming by 2023 it's expected to be over 90 billion in US dollars. So yeah AVR manufacturers want a piece of that pie for sure.
They certainly want a piece, but it's not going to happen without offering more diverse video ports at the back panel. Ever. For consoles, HDMI only is fine. Consoles do not offer any other interface anyway. For PC world, they will need to put more effort to evolve boards and offer DisplayPort too. See this post for what AVRs need to develop to be truly competitive in this market.
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Do not forget that audio solutions in PC world are very diverse and competitive already, from onboard ever improving audio, to add-in cards like sound blaster, to multi-channel desktop systems, soundbars, etc. AVRs would need to offer a good value, attractive connectivity and feature appeal to become more popular in that market. With HDMI ports on offer only, this is not possible. A simple restriction is number of combinations of resolutions and refresh rates in AVR's EDID, which is mostly restricted to 1080p and 4K only due to traditional focus on consumer electronics sector. Most AVR machines do not support 1440p, let alone more diverse screen settings. This is automatically a no go for PC people and they will avoid AVRs and favour direct DisplayPort connections, without elaborate workaround for sound. AVRs' HDMI boards are not well-suited at this moment to integrate into PC ecosystem.
As for revenue money, almost $90 billion is just mobile gaming worldwide. The figure is much higher across platforms. It's an exploding industry. See below.