Alignment QC differences between HISAT2 and Qualimap
89038751 pairs times 2 is 178 million reads. That times the approximately 97% alignment rate is around 172 million reads, which is what qualimap is reporting.

A "non-unique" alignment is one that can map to multiple places (either equally well, or where all of the alignments are of similar enough quality). Such alignments have a single "primary" alignment and one or more "secondary" alignments, which is where the "secondary" metrics come from.

For the qualimap output, there are additional metrics describing how reads overlap genes (or not). Of note are the "ambiguous" alignments, which are those overlapping multiple genes. "No feature" metrics, then, refer to alignments not overlapping any gene (see the qualimap documentation for further details).

My guess is that you have such a high "intergenic" rate because you've either used the wrong GTF file or have told qualimap the wrong strand setting. For unusual organisms one expects many reads to arise from unannotated genes. This is not the case for common model organisms, such as mice and humans, where there are very few remaining commonly expressed unannotated genes.