My 2 cents:
Limitations
As a limitation: Walking speed should be slower on land. Maybe only 20-25 ft, rather than the standard 30? But they can get a 30 ft swimming speed, or even more.
How do Pengoi deal with heat? Should they get any disadvantages when fighting in a desert: dry land & hot sun?
Ability score increase
Dex is a really difficult one. On land, they are clumsy and slow, so you'd almost have to give a penalty (but don't: penalties on ability scores suck). But in water, they are agile. I wouldn't touch Dex, just to avoid such a discussion.
But they can swim huge distances, survive the cold easily, so perhaps a Con bonus makes sense? Maybe even resistance to cold damage? If you base of off the Emperor penguin - the one that stands in antarctic blizzards for months - you should consider immunity to cold damage!
And they know how to survive, so a Wis bonus, and perhaps a proficiency in survival would make sense?
Finally, penguins are soooo cuuuute! So, I could defend a Cha bonus.
Other bonuses
You can probably get away giving them Fey Ancestry (advantage saving against charms).
Culture
I would not think they have a rich culture. Nomadic culture, in large packs. But not much art.
They could be from the barren (ant)arctic islands where they live of fishing. Are they partners or enemies of the Merfolk?
The logical gods that link with the arctic conditions would be Talos (storms), Auril (winter) and especially Umberlee (the sea/ocean). However, all those gods are evil! Do the Pengoi therefore use their cuteness as a deception to hide their true nature, which is frequently evil, even chaotic evil? Or are they the good side in a harsh ash and evil environment?