<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-03-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001439404</issuerCik>
        <issuerName>ZYNGA INC</issuerName>
        <issuerTradingSymbol>ZNGA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001739097</rptOwnerCik>
            <rptOwnerName>Ryan Jeffrey Miles</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ZYNGA INC. 699 8TH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94103</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief People Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <securityTitle>
                <value>Class A Common Stock</value>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionCode>M</transactionCode>
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            </transactionCoding>
            <transactionTimeliness>
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            </transactionTimeliness>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
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    </nonDerivativeTable>

    <derivativeTable>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each restricted stock unit represents a contingent right to receive 1 share of the Issuer's Class A Common Stock upon vest.</footnote>
        <footnote id="F2">Represents shares sold to satisfy tax withholding obligations in connection with the vesting of the restricted stock units described in Table II.</footnote>
        <footnote id="F3">25% of the shares subject to the award vested on March 15, 2020, and 6.25% of the shares subject to the award vest quarterly thereafter, generally subject to continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F4">25% of the shares subject to the award vested on March 15, 2021, and 6.25% of the shares subject to the award vest quarterly thereafter for a period of four years after the commencement date, generally subject to continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F5">Amounts represent the actual number of earned shares subject to the performance stock unit award, as determined by the Issuer's board of
directors.</footnote>
        <footnote id="F6">Each PSU represents a contingent right to receive a share of the Issuer's Class A common stock based upon the achievement of a specified financial metric (the Issuer's annual operating cash flow). Once the number of earned shares (if any) subject to the PSUs have been determined, 25% of the earned shares will vest on March 15, 2021, and 6.25% of the earned shares will vest quarterly thereafter, generally subject to the reporting person's continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F7">25% of the shares subject to the award vested on March 15, 2022, and 6.25% of the shares subject to the award vest quarterly thereafter, generally subject to continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F8">Each PSU represents a contingent right to receive a share of the Issuer's Class A common stock based upon the achievement of a specified financial metric (the Issuer's annual operating cash flow). Once the number of earned shares (if any) subject to the PSUs have been determined, 25% of the earned shares will vest on March 15, 2022, and 6.25% of the earned shares will vest quarterly thereafter, generally subject to the reporting person's continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F9">6.25% of the shares subject to the award will vest on June 15, 2022, and 6.25% of the shares subject to the award vest quarterly thereafter, generally subject to continued service to the Issuer through each vesting date.</footnote>
        <footnote id="F10">Each PSU represents a contingent right to receive a share of the Issuer's Class A common stock based upon the achievement of a specified financial metric (the Issuer's annual operating cash flow). Once the number of earned shares (if any) subject to the PSUs have been determined, 25% of the earned shares will vest on March 15, 2023, and 6.25% of the earned shares will vest quarterly thereafter, generally subject to the reporting person's continued service to the Issuer through each vesting date. The number of shares reported herein is a target number, and the actual number of shares issuable pursuant to the PSU will range from 0-150% of the number of target shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Matt Tolland, as attorney-in-fact for Jeffrey M. Ryan</signatureName>
        <signatureDate>2022-03-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
