and where would I find that in Puerto Plata ?
I believe those are Ikea products, so not in POP.
Having raised two kids in POP, while I don't know this, I doubt you would find a gate like this locally... We have never had one, so I have never even looked anywhere. I would personally either try in Santiago (Ikea or others) or order online. For any security things (as a gate is), I would also check carefully the quality of anything in local offer. The weight of such an item should not be that much, so with a courier you could perhaps have on in your hands within a week or less ordering online...
There are or used to be two baby item stores on the Beller near Centro Medico Bournigal (which is on the other side of the public school), but again, not sure if they had anything like this....