Script for concatenating delimited text files
There is some repetition between your header-reading routine and the rest of the code.  You could incorporate it into the main loop to remove that duplication and avoid opening the first file twice.  You already use next(reader) nicely to read the header; use the same technique to skip the header row.

To determine the seed from a file path, you look for a - in the file path.  Your glob should have a - to ensure that that succeeds.

import csv
from glob import glob

paths = glob('*-*/unknown/*.dat')

with open('output.dat', 'a') as csv_output:
    writer = csv.writer(csv_output, delimiter='\t')
    header_written = False

    for path in paths:
        param_dir = path.split('/')[0]
        seed = param_dir.split('-')[0]

        with open(path, 'r') as csv_input:
            reader = csv.reader(csv_input, delimiter='\t')

            header = next(reader)
            if not header_written:
                writer.writerow(['seed'] + header)
                header_written = True

            for row in reader:
                writer.writerow([seed] + row)