How can he compel the seller to cancel the new auction and sell him the item as they contracted to do?
Expectation damages are the typical remedy for breach of contract
The general measure of damages for breach of contract is expectation damages: "the plaintiff will be entitled to the value of the promised performance" (Bank of America Canada v. Mutual Trust Co., 2002 SCC 43 at paragraph 26); "the purpose of expectation damages is to put the plaintiff in the same position it would have been if the contract had been performed (Grandeur Homes Inc. v. Zeng, 2021 ONSC 4005 at paragraph 19).
This is a general principle of common-law contract law rooted in English jurisprudence. See Robinson v. Harman (1848) 1 Ex. 850, p. 855:
The rule of the common law is, that where a party sustains a loss by reason of a breach of contract, he is, so far as money can do it, to be placed in the same situation, with respect to damages, as if the contract had been performed.
This was recently confirmed by the U.K. Supreme Court in Morris-Garner v. One Step (Support) Ltd.,  UKSC 20:
Damage for breach of contract are ... a substitute for performance. That is why they are generally regarded as an adequate remedy. The courts will not prevent self-interested breaches of contract where the interests of the innocent party can be adequately protected by an award of damages.
Specific performance is not usual
Specific performance (cancelling the new auction and forcing the first sale) is an exceptional remedy for breach of contract. Specific performance is an equitable remedy. As an equitable remedy, it is always discretionary; the wronged party does not have a right to specific performance.
Specific performance may be ordered when:
- expectation damages are inadequate as a remedy
- where the contract was for a sale of a particular piece of land (but even this has been limited in some jurisdictions to circumstances where the property is particularly unique)
- difficulty in quantifying damages
Specific performance is typically not ordered when a substitute is available by which expectation damages would be demonstrated.
See generally Chitty on Contracts, §30-015–30-025.