The pictured warship is called "Mekura Bune" or "Blind Ship". It is about as large as the smallest class of Japanese warship (i.e. Kobaya) and armed with what are essentially anti-personnel deck sweepers. Incidentally, Japanese also called Korean Turtle Ship with the same name.
Mekura Bune is simply too small to stand up against Korean warships which were generally larger than their Japanese counterparts and armed with significantly more powerful cannons.

In fact, I doubt even the largest and most powerful of the Japanese warships, the Tekkousen (Iron-armored O-atakebune) had the firepower to match up with a typical Korean Panokseon, although it could survive an encounter with one thanks to its plating and sheer bulk prevent it to be sunk outright.

For example, Kuki Yoshitaka's "Nihonmaru" flagship had THREE cannons and it was a supremely impressive warship by Japanese standard. A 16th century Turtle ship had at least TWELVE cannons (six on each side, plus one at the head and another a the tail) of varying sizes. Japanese ships were hopelessly outgunned, and that's before we consider potential Chinese involvement (who had even more deadly guns and warships).

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Now, European involvement would certainly make Yi Sun Sin's live more difficult, but it wasn't an insurmountable problem (European seafaring vessels will have problems at Korean coasts, at the mercy of wind, and they were few in numbers), and ultimately it doesn't matter in the grand scheme as Imjin War was mostly fought, and decided, on land.