I personally am tempted to say no, but ultimately I think it'll be best to have democracy decide.
Also, purely on the basis of technicality, every vintage console of eligible for this thunderdome has a way of using the soundchip to play raw PCM audio, which is another argument for being inclusionist here. I've seen plenty of people over the years be weirdly stuck-up about chiptune puritanism in its various forms, and I don't want to encourage that. If it sounds like a chiptune to you, then it's a chiptune for the sake of the dome.
This approach also helps avoid a bunch of weird, pedantic rules-lawyering over edge cases: e.g. one could be a prick and argue the
Game Boy songs from Tetrisphere aren't chiptunes because there's evidence of a soundchip being emulated, but that would be obnoxious (these songs would be eligible btw, though I'll have to adjust my definition of "modern" to include throwbacks like this, even if the system was still technically active at the time). Likewise, one could argue that
this song from the PC-Engine CD port of The Manhole it not a chiptune because it's
technically redbook audio, even though common sense tells us it was composed using the NES sound chip (note: this song would be ineligible though for being a remix of the PC-Engine Batman stage 1 theme (though I guess it would qualify as "modern" since it's acting as a stylistic throwback in this case)).
"Original" is probably the criteria I'll be the most fussy about, though if you believed the song was original but it turns out to be a remix of some obscure Japanese-only doujin STG or something I'll let it fly.
tl;dr listen to your heart