Updating a list item works in a similar manner to creating a new item. Replace the _updateListItem function with the following code:
private _updateListItem(): void { const url: string = this.context.pageContext.site.absoluteUrl+ "/_api/web/lists/getbytitle('My List')/items(1)"; const itemDefinition : any = { "Title": "Modified title field value!" }; const headers : any = { "X-HTTP-Method":"MERGE", "IF-MATCH": "*", }; const spHttpClientOptions: ISPHttpClientOptions = { "headers": headers, "body": JSON.stringify(itemDefinition) }; this.context.spHttpClient.post(url, SPHttpClient.configurations.v1, spHttpClientOptions) .then((response: SPHttpClientResponse) => { if (response.status === 204) { this._operationResults.innerHTML = "Update: List Item updated...