Does a direct rollover from a 401(k) to open a Traditional IRA count as a contribution?

A direct rollover into an IRA is not considered a contribution and does not have to be reported when filing your taxes.

A rollover from a 401(k) to a traditional IRA is not a contribution and is not to be entered anywhere under Deductions & Credits.  However, this rollover is required to be reported even though it is nontaxable.  The gross amount must appear on Form 1040 line 5a but will be excluded from the taxable amount on line 5b.

So I filed my tax return a few hours before I saw your reply, and after downloading the PDF of the return, I can see that box 5a of Form 1040 is blank. Will reporting this amount to the IRS require me to amend this tax return within the next year, or is there another way to report it?

I should have qualified my previous reply.  Line 5a of Form 1040 will be blank if the entire amount distributed from the 401(k) is taxable and appears on line 5b.

Line 5b is also blank. The amount of the rollover contribution was over $7K, and I'd get taxed if I try to take a distribution from the account.

Will I have to amend my tax return to report an amount, or is there another way to report the exact amount to the IRS?

It seems that you did not report this rollover on your tax return.  There is no good way to report this by filing an amended tax return because it changes nothing but what should have been on Form 1040 line 5a and there is no equivalent on Form 1040-X.  Rather than amend your tax return, it would probably make sense to just retain the documentation necessary to show the IRS that the rollover to the traditional IRA was completed, should the IRS question the transaction.