Read counts from BAM file
Your data is not aligned to hg19, but to a bunch of RNA ref sequences. If you would align to hg19 you'll get each chromosome instead of the NR_* or NM_* accession codes with your samtools view -H code. With samtools idxstats file.bam you'll get the reads per chromosome (or per nucleotide sequence in your case).

For use in featureCounts my advice is to get the fastq files, and align it yourself to hg19 (or hg38 to be more up to date).

If your data is properly aligned to hg19 your output should be something like this:

samtools view -H aligned2hg19.bam

@SQ SN:chrM LN:16571
@SQ SN:chr1 LN:249250621
@SQ SN:chr2 LN:243199373
@SQ SN:chr3 LN:198022430
@SQ SN:chr4 LN:191154276
@SQ SN:chr5 LN:180915260
@SQ SN:chr6 LN:171115067
@SQ SN:chr7 LN:159138663
@SQ SN:chr8 LN:146364022
@SQ SN:chr9 LN:141213431
@SQ SN:chr10    LN:135534747
@SQ SN:chr11    LN:135006516
@SQ SN:chr12    LN:133851895
@SQ SN:chr13    LN:115169878
@SQ SN:chr14    LN:107349540
@SQ SN:chr15    LN:102531392
@SQ SN:chr16    LN:90354753
@SQ SN:chr17    LN:81195210
@SQ SN:chr18    LN:78077248
@SQ SN:chr19    LN:59128983
@SQ SN:chr20    LN:63025520
@SQ SN:chr21    LN:48129895
@SQ SN:chr22    LN:51304566
@SQ SN:chrX LN:155270560
@SQ SN:chrY LN:59373566