Who pays the fees to JAMS Inc. (US$1,750+) for mandatory arbitration?

Who pays the fees?

It's a filing fee. So whoever files, pays the fee. Of-course, you may want to be reimbursed for this if the arbitration concludes the onus is on the other party and not on your side. But that's part of the resolution, not the initial filing.

Do note, you suggest the filing fee would be 1,500 minimum. For a business-to-business problem, this would be correct. However, I'm assuming you're more interested in disputes between users and Stack Exchange. Users would be consumers, not a business (unless we're talking about Teams here, in that case you'd be correct).

The full text of the section you linked to (emphasis mine):

For two-party matters, the Filing Fee is $1,500. For matters involving three or more parties, the filing fee is $2,000. The entire Filing Fee must be paid in full to expedite the commencement of the proceedings. Thereafter, a Case Management Fee of 12% will be assessed against all Professional Fees, including time spent for hearings, pre- and post-hearing reading and research and award preparation. JAMS also charges a $1,500 filing fee for counterclaims.

For matters involving consumers, the consumer is only required to pay $250. See JAMS Policy on Consumer Arbitrations Pursuant to Pre-Dispute Clauses. For matters based on a clause or agreement that is required as a condition of employment, the employee is only required to pay $400. See JAMS Policy on Employment Arbitrations, Minimum Standards of Fairness.

A refund of $600 will be issued if the matter is withdrawn within five days of filing. After five days, the filing fee is non-refundable.

User versus SE: $250
Employee versus SE: $400
Business versus SE: $1,500
Multiple businesses versus SE: $2,000

For completeness sake: should SE feel that they have a dispute with you and they end up with filing, the filing fees are on them. Those will probably be $1,500, regardless of who they have a problem with.

The JAMS website was recently updated with relevant information. If the user is a "consumer"...

With respect to the cost of the arbitration, when a consumer initiates arbitration against the company, the only fee required to be paid by the consumer is $250, which is approximately equivalent to current Court filing fees. All other costs must be borne by the company, including any remaining JAMS Case Management Fee and all professional fees for the arbitrator's services.
_{Consumer Minimum Standards}

This does not apply to JAMS Inc.'s international arbitration:

For two-party matters, JAMS charges a $1,750 Filing fee, to be paid by the party initiating the Arbitration. JAMS also charges a $1,750 Filing Fee for counterclaims.

The recent legal case Terrell Abernathy, et al. vs. DoorDash Inc. (2020) gives precedent:

Petitioners are 5,879 couriers who work for respondent, DoorDash, Inc. In order to make deliveries for respondent, petitioners allegedly each clicked through a contract that contained a “Mutual Arbitration Provision, ...

Inturn, AAA’s Commercial Arbitration Rules require each individual to pay a filing fee of $300 and the responding company to pay a filing fee of $1,900.

... petitioner couriers have now filed an amended motion to compel arbitration with the AAA which seeks to compel arbitration on behalf of 5,879 individuals ...

The motion to compel arbitration is GRANTED as to the 5,010 petitioners who submitted declarations. DoorDash is ordered to immediately commence AAA arbitration with these petitioners. The motion is DENIED as to the 869 petitioners who submitted mere witness statements.

It's not the same company as Stack Exchange chooses, but it's similar.

(I also suspect the 5,010 * $1,900 = $9.5 million in filing fees is only the tip of the iceberg in terms of costs. E.g., legal fees, work hours. [Putting aside what happens if they don't "win" every single case.])