@KennethT, I followed your link for Sanuria and went to the "Street View" on Google. The view shows the awning with Chinese ideograms on it which (on the left) is more-or-less an onomatopoeia for "Sanuria" and on the right says "small eats shop/stall" = smaller-scale restaurant. I would say this pegs the owners as of Chinese ethnicity or heritage. I doubt any ethnic-Malay-owned shop would put Chinese ideograms on their frontage, except in special circumstances.
I also looked around and found this: http://www.menupages.com/restaurants/sanur/menu
If this indeed looks like what you also were looking at then I would say most of the stuff on offer is Malaysian-Chinese cuisine, plus standard Malay-type dishes as interpreted by Malaysian Chinese folks. I would not peg it as a "Malay cuisine" place. The "Indonesian" stuff I would speculate would be sort-of similar dishes as found in "Indonesia", interpreted through the owner's lens. There may be some Nyonya-type influences too.
I plugged in "malay restaurant" into a google map search and got this: https://www.google.com/maps/search/malay+restaurant/@40.7052248,-74.0494413,12z/data=!3m1!4b1
Laut - my understanding was that when it first opened years ago it was much more attuned to Malay cuisine ( @Pan, can you confirm or deny this, please?) but when I look at the menu now it looks like a HUGE mash-up between Malaysian-Chinese, sort-of Thai, sort-of Malay, plus this-and-that. The "Nyonya" restaurants do serve Nyonya-derived if not always true Nyonya dishes plus the usual mash-ups for a restaurant of this sort in a Western place. Most of the others (if not all) seem to hew more to Malaysian-Chinese cuisine than not.
(p.s.: Hainanese Chicken Rice is NOT a Nyonya dish even if it is offered in the "Nyonya" restaurants in NYC.)
Just as an aside: If one walks into a Malay house, or an actual Malay restaurant, there is often what can only be described as a "Malay smell". I suppose this might be interpreted as somewhat...umm...politically incorrect, but folks who grew up around those parts "know" what is meant here.