pyvcf is parsing VCF files, I am looking for a parser for VCF/BCF stats files generated by bcftools stats.

"These text stats files contains some tab delimited tables and key value pairs ..."

At least for tab delimited tables this is a more general issue that goes beyond this particular tool. The Pandas package is one of the main tools in the structured data space of the Python ecosystem.

Indeed, it looks like Illumina's Haplotype VCF comparison tools hap.py tools has a function parseStats in bcftools.py that is just collecting lines starting with SN and converting the data into a Pandas DataFrame for further analysis with Pandas:

def parseStats(output, colname="count"):
    """ Parse BCFTOOLS Stats Output """

    result = {}
    for x in output.split("\n"):
        if x.startswith("SN"):
            vx = x.split("\t")
            name = vx[2].replace("number of ", "").replace(":", "")
            count = int(vx[3])
            result[name] = count

    result = pandas.DataFrame(list(result.iteritems()), columns=["type", colname])
    return result

It looks pretty portable/adpatable. Is that all you need?
The original post mentioned some "key value pairs", but I don't see that handled.