Consider a Steam Link, http://store.steampowered.com/app/353380/ or similar system to mirror the content from your PC. It will handle sending video/audio to your TV/arcade and sending the inputs back the desktop.
I have one of those lying around, but the issue afaik is that the Steam Link kind of takes over the PC that is running the games to stream the system. Hooking up the speaker/controls/VGA of my arcade via a long cable directly to my PC, means Windows sees it as another screen with more devices.
Then I just tell VMWare Workstation that the arcade joystick USB should go directly to the arcade VM, and drag the VM window over to the arcade screen. This means I can use my computer directly as normal (I code in a linux VM on it), while the arcade is running independently. It works really well and lets me use a spare 4ghz core to run Hyperspin+MAME faster than my old arcade PC ever did.
How much latency does one of these add? It might be fine on a modern cinematic console shooter, but a large amount of the appeal of some old arcade games is their frame-perfect timing. I can't imagine that's helped by adding a round trip over the network, not to mention streaming the video back. That's gotta add 2-3 frames' latency at the very least.
The default settings have some noticeable latency (5-10ms), but changing the video encoding from "balanced" to "fast" drop it down to almost nothing. You can additionally plug the controller(s) into your PC to further remove any input delay. I can't vouch for emulated arcade games, but it works surprisingly well with a steam collection.
You want to make sure that you have the Steam Link wired into your network, rather than on wireless, because that makes a huge difference.
Otherwise, it's gotten so they are pretty decent now. When the Links first came out, they were quite laggy and unstable, but after a hundred or so patches, it's settled down.
I'm modding my old iCade cabinet to make a bartop with an 8" LCD monitor, and I opted to use an Atom based stick PC. I'm going to use the stick PC for running retro emulation locally, and streaming from Steam via the Windows Steam client.
I'm also going to use an HDMI switcher so that I can connect it to a faster machine like my laptop as an option.
