Why does this half-bridge mosfet not short to ground?
Q1 and Q2 are a pair driving an inductor to form a buck (step-down) DC-DC converter.

There are two phases of operation:


Q1 on: current flows into the inductor L and load, meanwhile the inductor stores energy (builds flux)
Q2 on: inductor L energy released, current flows into load as the flux collapses


The key is, neither Q1 or Q2 are kept on long enough such that a short can occur; the current though L is a sawtwooth that averages out to the charging current being delivered to the load. This is true so long as Q1, Q2 and the bq24650 IC are working correctly to deliver the charge current.

That said, you're right in observing that if Q2 stayed on, the battery would be connected as a short-circuit through the inductor L. That's not likely as the IC controls the Q2 gate, but it's a possible failure mode to consider.