"Space weapons" here most likely means some combination of anti-satellite weapons and electronic warfare such as GPS jammers. AFAIK it's been widely believed that the USSR/Russia has had these capabilities in orbit since the 80s. I'd be willing to bet that the US has had them for decades as well, it just hasn't been publicly acknowledged.

For some reason they did not provide any details beyond that they have kinetic and non-kinetic means. Kinetik indeed can mean just ability to blow up satellites but IMHO it is good enough to trigger an arms race.