Scopes are usually 1 meg impedance, or 10 Meg with a x10 probe, a modern digital meter is 10 Meg - older analogue meters vary according to range, and are higher than 10 Meg on the highest ranges (but considerably less on the lower ones).The meter is probably showing an RMS value and there could be some differences in loading. A scope typically has a higher impedance than a meter.
Like I said, crude attempt at class CNote that the two output transistors are acting as a half-wave rectifier. They do not conduct during the sinewave negative half-cycle. The resonant tank is being excited by a series of half-sine pulses. These a re probably closer to squarewave pulses because the transistors are operating at their maximum gain.