It's always fascinating to see what types of games other countries and cultures prefer. While I'm unfamiliar with most of the Japanese games, I can say that while I understand the love for Dragon Quest III, and can totally see it bagging the top spot on a 'games released in 1988' list, I think much of that love comes from it being more accessible than Dragon Quest II (which was hard as hell, and twice as unforgiving as the original). The twist at the end, where you discover you've been playing a prequel to the original Dragon Quest all this time, was nicely done as well.
I'd have a very difficult time ranking them in any specific order, but my own personal best list of games from '88 would include:
The Guardian Legend - What do you get when you mix a vertically-scrolling corridor shooter with a top-down action/adventure game? This title, right here, which still deserves a sequel but will never get one, because nobody has any idea who owns the rights to it thirty years later.
Mega Man 2 - Like Kitunebi, this is my favorite Mega Man game. It definitely has the best soundtrack of all the 8-bit titles.
Splatterhouse - Yeah, the US arcade release happened in 1989, but if Kitsu can roll with Japanese release dates, then so can I. This gave me nightmares as a kid, but helped usher in my enjoyment of the horror genre. To this day, I can still remember images from dreams I had after playing this game.
Battle Chess - I didn't own a PC back when this came out, but several friends did, and it was always a blast to load up and play at their houses. As one of the only girls in my grade school chess club, just knowing this existed provided me with some essential street cred when dealing with other nerds.
Super Mario Bros. 2 & 3 - Pretty much for the same reasons. Even if Mario 2 isn't a "real" Mario game, it's still fun as hell with tons of variety thanks to the four playable characters, and I loved not having a timer for once, which lets you play around and explore to your heart's content instead of concentrating solely on reaching the end of the stage.
Phantasy Star - Such a complete departure from the standard swords & sorcery fare of most RPGs. I loved that this one gave you multiple party members and was set in a high-tech, science-fantasy setting instead of the normal medieval-esque times you usually saw. Plus, the first RPG I ever played where the protagonist was canonically female instead of it just being an option you could pick, like in the various Gold Box games from SSI. Somewhere my brother probably still has the graph paper maps we made of all the dungeons.
Contra - More two-player run-and-gun action. We actually never owned this game ourselves, but a family friend had it and you could blast through it in about 20 minutes with the 30-life code, which we generally did at least once when we were over there.
Blaster Master - We picked this one up at a neighborhood rummage sale for a few bucks. While it's no Ninja Gaiden, it's still one of the most difficult games I think I've ever played on the NES. Of course, what's difficult to one gamer is a piece of cake to another, and I'll never forget watching as a family friend literally demolished this game while playing it blindfolded. That's a feat I'll never bother to attempt, and I'd never believe it if I hadn't been sitting there in the room watching it with my own eyes, but holy crap, was that ever humbling. Probably why I enjoy watching speedruns so much today.
Bionic Commando - At first, I hated this game because it was a platformer without a jumping mechanic. This made little sense to me, and the controls for the arm felt confusing and awkward. Add to that what felt like an enormous difficulty spike once you got past the first Neutral Zone, and I was mainly reduced to watching friends play this. Then, for whatever reason, one day I picked it up again, and suddenly everything just clicked. I tore through the game in one single, epic play session, feeling like I was one with the arm. I don't think killing Hitler has ever been so fun as it was that Summer afternoon.