I'm not sure I trust the Q/A which states the hose is 1/8" NPT, but you should be able to take that hose to a hardware store and come up with adapters to thread the matching quick release air fitting to the hose to match that tool. There are "automotive," "industrial," and I think a universal; that tool looks to use the "industrial." Hardware stores will mostly have the whole gamut. There is some possibility that it's a metric thread which for reasons of convention in... there I go assuming things. If you're in the USA, air fittings are rarely if ever metric, so it may take a more specialized hardware store or even a place that specializes in hoses and fittings to dig up what you need. But any hardware store will at least have a display that will help you determine what that thread is and may be able to advise you on local resources if they don't have it.

I would say that I'm confused that you want to use that tool; this compressor has no tank, so having a triggered air hose (meant to stop airflow from a reservoir and release on command) doesn't really make sense.

I would use one of the simpler schrader-to-presta adapters, or if your intent is to take advantage of the compressor's auto-off and not have to hold it in place, at least find a presta-compatible tool that doesn't include a separate valve (nor would the gauge seem to do you any good since the compressor already has one and is set to shut off at a specific pressure).

This would enable you to use that compressor without adding the tool at all and would stay threaded together for auto-shutoff: https://www.amazon.com/Bike-Bits-Brass-Presta-Adapter/dp/B07DN2MTKQ/ref=sr_1_19

I prefer this type, which doesn't have to be threaded on/off the presta valve, but has to be held in place while filling. This makes it easier to use if you have a tank of compressed air and thus only take a few seconds to fill. https://www.amazon.com/Presta-Adapter-Chain-Floor-Spare/dp/B000X63JUO/ref=sr_1_16

You may also get better answers over in a cycling subreddit; presta valves don't turn up in the car world.