As non resident alien receiving grants from Google would I be elligible to receive stimulus checks if I register an itin?

Filing a tax return with an ITIN will not help you get a stimulus payment. People without Social Security Numbers (that were issued before the due date of the tax return) are not eligible for the stimulus payments. (People filing tax returns with ITINs cannot claim the credit. Couples filing jointly with one having an SSN and the other having an ITIN can only claim the credit for one person.)

Not only that, but nonresident aliens are not eligible for stimulus payments. And if you never had a green card (thus don't pass the Green Card Test) and don't spent time in the US (thus don't pass the Substantial Presence Test), you are a nonresident alien for tax purposes, and you won't get stimulus checks and cannot claim the credit on 1040-NR, even if you had an SSN. Some people who previously worked in the US got the stimulus checks (the advance payment), because they were resident aliens with SSNs in the past year whose tax returns were used for determining eligibility for the checks.

You can read this from the text of the law for EIP 1, 26 USC 6428, as amended by the December 2020 stimulus law. (The law for EIP 2, 26 USC 6428A, added by the December stimulus law, is not yet consolidated into the US Code yet. The proposed law for EIP 3, in 26 USC 6428B, is not yet passed as of this writing. The text for those are all slightly different, but for the issues discussed here they are basically the same as EIP 1.)

Subsection (d)(1) provides that nonresident aliens are not eligible:

(d) Eligible individual

For purposes of this section, the term "eligible individual" means any individual other than-

(1) any nonresident alien individual,

Subsection (g)(1 and 3) (as replaced by the December law) provides that people without SSNs are not eligible:

(g) Identification Number Requirement.--

(1) Requirements for credit.--Subject to paragraph (2), with respect to the credit allowed under subsection (a), the following provisions shall apply:

(A) In general.--In the case of a return other than a joint return, the $1,200 amount in subsection (a)(1) shall be treated as being zero unless the taxpayer includes the valid identification number of the taxpayer on the return of tax for the taxable year.

(B) Joint returns.--In the case of a joint return, the $2,400 amount in subsection (a)(1) shall be treated as being--

(i) $1,200 if the valid identification number of only 1 spouse is included on the return of tax for the taxable year, and

(ii) zero if the valid identification number of neither spouse is so included.

[...]

(3) Valid identification number.--

(A) In general.--For purposes of this subsection, the term `valid identification number' means a social security number (as such term is defined in section 24(h)(7)).

[...]

I don't know what the situation was with the story you referred to of the French woman. The article does not detail her status or her husband's status. If she was a US citizen or ever had a green card (and thus would be a resident alien), then her receiving the stimulus payment would be normal. The mention of being in the "database of American social services" seems to indicate that they are talking about some kind of Social Security benefit. There is a section in the law that deals with stimulus checks for Social Security beneficiaries who have not filed taxes, in subsection (f)(5)(B)(i):

(5) In the case of an individual who, at the time of any determination made pursuant to paragraph (3), has not filed a tax return for the year described in paragraph (1), the Secretary may-

[...]

(B) if the individual has not filed a tax return for such individual's first taxable year beginning in 2018, use information with respect to such individual for calendar year 2019 provided in-

(i) Form SSA–1099, Social Security Benefit Statement, or

[...]

From what I know SSA-1099 should be sent to US citizens and resident aliens, and SSA-1042S should be sent to nonresident aliens (as they have tax withholding differences). Since the woman has a foreign address, they would have had to determine whether she was a resident alien at some point. I don't know how she would have gotten SSA-1099 if she was not a resident alien.