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.
Do you mean that you can't convert the installation to use Schrader valves, or that you cannot use an adapter between the Presta valve and the Schrader chuck? I believe sllewgh is referring to these, which allow you to retain your Presta valves but fill them with a Schrader chuck: https://www.amazon.com/Bike-Bits-Brass-Presta-Adapter/dp/B07DN2MTKQ/ref=sr_1_19