With the advent of HTTP Adaptive Streaming (HAS) technology, the visual quality of videos streamed over the Internet has become a paramount Key Performance Indicator (KPI) for Internet Service Providers (ISPs), who want to deliver a high video streaming Quality of Experience (QoE) to satisfy their customers and avoid churn. We address the problem of real-time QoE monitoring of HAS, from the ISP perspective, focusing on video-resolution, video bitrate and re-buffering prediction. Given the wide adoption of end-to-end encryption, we resort to machine-learning models to predict these metrics in a fine-grained scale, using as input only packet-level data. The proposed measurement system performs predictions in real time, during the course of an ongoing video-streaming session, with a time granularity as small as one second. We consider the particular case of YouTube video streaming. Empirical evaluations on a large and heterogeneous corpus of YouTube measurements demonstrate that the proposed system can predict six different video resolution levels with very high accuracy -- from 144p to 1080p, estimate the video encoding bitrate as a regression problem with small estimation errors, and predict the occurrence of re-buffering events with high precision and recall, all of this in real time. Different from state of the art, the prediction task is not bound to coarse-grained video quality classes and does not require chunk-detection approaches for feature extraction. As an additional novelty, our methodology continuously extracts features from the encrypted stream of packets in a stream-like, recursive manner, using bounded - and lightweight - memory footprints; this enables its execution on top of limited memory hardware, such as set-top boxes or home routers, which are nowadays the most preferred devices for conducting end-customer monitoring by major vendors.