I think it is fairly clear from that article, and the ones linked from it what the concern is. The last paragraph sums it up pretty well I think (bold me for emphasis):
"ARM is a chip architecture designer that licenses the designs out to parties interested in incorporating the designs in their own silicon. Among ARM's licensees are Apple, Samsung, Broadcom, Qualcomm, Huawei HiSilicon, Nvidia itself, and more, with its chip designs in almost every smartphone currently in the consumer's hands. Apple's latest M1 chip also contains ARM technology. The concern is that Nvidia's ownership of ARM would give it too much power over its competitors."
Quite frankly ARM is everywhere.
If I were one of those companies other than NVIDIA using ARM designs I wouldn't be comfortable with NVIDIA's "vow to maintain ARM's neutrality and its open licensing model" without some significant legal teeth behind it. Maybe there is some protection in the exiting ARM licensing but in all the articles I read on the topic no one seems to be suggesting that.
I don't have an opinion as to whether or not NVIDIA should have been allowed to buy ARM or not, but they could put significant pressure on competitors to either pay them more to continue to license ARM or lock them out of ARM technologies when licenses expire.
The other part here in some of the voices seems to be UK pride in the ARM legacy. Nothing wrong with that, but if the companies find ARM less attractive to use because of this buy, and thus ARM is used less in new products, that certainly gives them reason to sound off. Not a reason to reverse the purchase, but I get it.