Open-source overhead photos of several newly built Chinese islands do not reveal sufficient space for runways capable of handling fixed-wing aircraft, nor do they appear to have sufficiently deep channels or long piers to accommodate the refueling and resupply of large warships. The islands are thus mostly ill-suited to sustain the kind of island-hopping campaign the US employed during World War II to gain dominance of the Western Pacific. The lack of such capability may be temporary as China succeeds in dredging enough infill around its larger claims to support paved runways.
Coast guard cutters and patrol boats are shallow-draft naval vessels that could berth at these artificial islands for short periods, but the islands are too small to store logistical supplies needed to replenish large task forces of deep-draft vessels. China is thus not making a serious attempt at this time to challenge the US Navy's preeminent freedom of navigation role in the area. The Chinese attempt at dominance is most likely economic in the short term: staking claims to fishing waters and oil exploration blocks.
The QZ article linked above correctly notes that China's legal claims to EEZs around the islands are weak, but China has shown an increasing disdain for international conventions such as UNCLOS or the need to seek international arbitration. The islands will eventually prove useful as way stations for crews of fishing boats and oil exploration vessels.
China is currently testing the will of its neighbors to confront its fishing and energy expeditions. More confrontations drive demand within China for a more robust blue-water navy, built around the 70-year old doctrine of aircraft carrier battle groups. A carrier battle group is designed to exert persistent control over geographic features called "choke points" that constrict naval movement. The Strait of Malacca is the nearest such choke point to China's island dredging campaign in the South China Sea. Control of the Strait of Malacca is the ultimate prize in this region.
Hainan Island is approximately 933 km from the Spratlys and 479 km from the Paracels, two island groups where China is most actively building artificial reefs. China may have a land-based capacity at Hainan to counter challenges to its possession of these islands in the absence of a mature carrier battle group. For example, its CJ-10 cruise missile can range 800 km and may be adaptable into an anti-ship variant. The CJ-10A air-launched variant can range over 2000 km, but its accuracy against sea-based targets with a conventional warhead is not clear.
The Chinese PLA Navy does not possess a base network comparable to the US possessions of Guam, Wake Island, Kwajalein Atoll, and other islands that support both naval and aerial expeditions. China will reveal just how seriously it takes its territorial claims when it switches focus from dredging tiny shoals to building the underway replenishment capability its PLA Navy will need (in the absence of larger bases) to support an expeditionary fleet.