It is an oversimplification to say lower frequencies have longer range. See Is free space path loss dependent on frequency? It's more accurate to say the range of a half-wave dipole decreases as frequency increases. But then so too does the size: a tiny half-wave dipole simply intercept less energy. Solution: antenna arrays, which become increasingly feasible as frequency increases.
Bandwidth is not frequency. Bandwidth is the difference between the lowest frequency and the highest frequency used by a radio signal.
There's another sense of "bandwidth" for digital communications: it's how fast bits can be sent. The two are related by the Shannon-Hartley theorem. Another variable in the Shannon-Hartley theorem is the signal-to-noise ratio. This is another thing limiting the range of WiGig: to achieve those high speeds requires a very good signal. Signal quality diminishes with distance as the radio signal spreads out due to the inverse square law.
Higher frequencies generally support higher bandwidth simply because there are more possible frequencies at high frequency. Are there more 5-digit numbers or 20-digit numbers?
For a real example, the amateur 40 meter band goes from 0.0070 to 0.0073 GHz in the US. Thus the bandwidth of the entire band is 0.0003 GHz. Since the entire band must support multiple users, the bandwidth of an individual signal is much less, typically 0.000004 GHz or less.
By comparison, the 23 centimeter band goes from 1.24 to 1.3 GHz, and so is 0.06 GHz wide. This makes it 200 times bigger than the 40 meter band.
A WiGig channel is 2.16 GHz wide, whereas WiFi is 0.02, 0.04, or 0.08 GHz wide. That makes the WiGig channel too wide to even fit in the same 2.4 and 5 GHz allocations used by WiFi, so the only option is to go higher in frequency, where there's room.
