Remote desktop software is not only outdated but not really cool or enjoyable to use.
An opinion, but ok ... I have used a similar system for karaoke that allows people to look in MY specific library for a song and then request it. Without a library link, the requestor(s) may be asking for things you can't play.
What do you mean by a "standalone local wi-fi hotspot version?" Do you mean desktop software of some sort? The monthly fee is $2/month which is relatively negligible and creating an event is fairly cheap relative to the revenue you most likely make per event.
Plus $5 per event .. I believe that is the charge that would be eliminated with a phone app through a temporary WiFi port (which everyone who has a Smartphone knows how to configure).
In response to all the people saying that they use Google Voice, it's an interesting way to take song requests but it's clearly limited relative to RequestNow's feature set. Google voice doesn't give you any way to organize your requests or easily answer them / let party-goers know when their song will be playing next.
Unless you're getting dozens of them (which you couldn't get to anyway) it doesn't appear to be marginally more difficult. Not sure anyone who takes multiple requests can tell someone when their song is playing until they play it anyway, but maybe that's a reason to use your software.