This claim is ridiculous. We know for a FACT that this version of possesses spider sense.
A) He tells Tony in Civil War that his senses were "dialed up to 11" and that he needs to wear the goggles to help him focus on what he needs to and not get overwhelmed by the sensory input. This is why Tony builds the expressive eye lenses into his improved Spidey costume. The fact that Peter continues to wear both costumes in Homecoming helps reinforce the idea that he needs them to help him control his spidey sense.
B) When Ant Man shrinks down and jumps on Caps shield while Spidey is holding it, his eyes widen and he starts looking around, saying "Hey guys, I think something is wrong" right before Ant Man grows big again, attacking SPidey and stealing the shield. It's clear that Peter sensed that he was in danger right before the attack happened.
C) When fighting Falcon and Bucky, Peter lands on some fixtures near the ceiling. When Bucky throws a piece of metal at Peter from behind, once again, we see the eye lenses widen and he says "Oh god!" before seamlessly dodging the metal and catching it. Once again, the film calls attention to him sensing something before it happens.
D) The trailer for homecoming shows him dodging punches from the "Avengers" thugs in a similar manner.
So yes, this version still has spider sense. In fact, based on his need to wear goggles that help him adjust to the sensory output, this version may have a more powerful spider sense than other versions we have previously seen. Jon Watts merely said that they didn't feel the need to mention it or specifically focus on it in this film, but he says that he's interested to explore that power in the sequel.
While I am slightly disappointed by the lack of focus on the spider-sense power, as it is one of Peter's more unique powers and it can look really cool when filmmakers show the audience how it helps him "see" differently, the creators have NOT removed this ability from his powerset. The titles of those articles are misleading and sensationalist.