Trying to understand store.dispatch argument as async function middleware at Redux

At redux source code in applyMiddleware,

import compose from './compose'
import { Middleware, MiddlewareAPI } from './types/middleware'
import { AnyAction } from './types/actions'
import {
  StoreEnhancer,
  Dispatch,
  PreloadedState,
  StoreEnhancerStoreCreator
} from './types/store'
import { Reducer } from './types/reducers'

/**
 * Creates a store enhancer that applies middleware to the dispatch method
 * of the Redux store. This is handy for a variety of tasks, such as expressing
 * asynchronous actions in a concise manner, or logging every action payload.
 *
 * See `redux-thunk` package as an example of the Redux middleware.
 *
 * Because middleware is potentially asynchronous, this should be the first
 * store enhancer in the composition chain.
 *
 * Note that each middleware will be given the `dispatch` and `getState` functions
 * as named arguments.
 *
 * @param middlewares The middleware chain to be applied.
 * @returns A store enhancer applying the middleware.
 *
 * @template Ext Dispatch signature added by a middleware.
 * @template S The type of the state supported by a middleware.
 */
export default function applyMiddleware(): StoreEnhancer
export default function applyMiddleware<Ext1, S>(
  middleware1: Middleware<Ext1, S, any>
): StoreEnhancer<{ dispatch: Ext1 }>
export default function applyMiddleware<Ext1, Ext2, S>(
  middleware1: Middleware<Ext1, S, any>,
  middleware2: Middleware<Ext2, S, any>
): StoreEnhancer<{ dispatch: Ext1 & Ext2 }>
export default function applyMiddleware<Ext1, Ext2, Ext3, S>(
  middleware1: Middleware<Ext1, S, any>,
  middleware2: Middleware<Ext2, S, any>,
  middleware3: Middleware<Ext3, S, any>
): StoreEnhancer<{ dispatch: Ext1 & Ext2 & Ext3 }>
export default function applyMiddleware<Ext1, Ext2, Ext3, Ext4, S>(
  middleware1: Middleware<Ext1, S, any>,
  middleware2: Middleware<Ext2, S, any>,
  middleware3: Middleware<Ext3, S, any>,
  middleware4: Middleware<Ext4, S, any>
): StoreEnhancer<{ dispatch: Ext1 & Ext2 & Ext3 & Ext4 }>
export default function applyMiddleware<Ext1, Ext2, Ext3, Ext4, Ext5, S>(
  middleware1: Middleware<Ext1, S, any>,
  middleware2: Middleware<Ext2, S, any>,
  middleware3: Middleware<Ext3, S, any>,
  middleware4: Middleware<Ext4, S, any>,
  middleware5: Middleware<Ext5, S, any>
): StoreEnhancer<{ dispatch: Ext1 & Ext2 & Ext3 & Ext4 & Ext5 }>
export default function applyMiddleware<Ext, S = any>(
  ...middlewares: Middleware<any, S, any>[]
): StoreEnhancer<{ dispatch: Ext }>
export default function applyMiddleware(
  ...middlewares: Middleware[]
): StoreEnhancer<any> {
  return (createStore: StoreEnhancerStoreCreator) =>
    <S, A extends AnyAction>(
      reducer: Reducer<S, A>,
      preloadedState?: PreloadedState<S>
    ) => {
      const store = createStore(reducer, preloadedState)
      let dispatch: Dispatch = () => {
        throw new Error(
          'Dispatching while constructing your middleware is not allowed. ' +
            'Other middleware would not be applied to this dispatch.'
        )
      }

      const middlewareAPI: MiddlewareAPI = {
        getState: store.getState,
        dispatch: (action, ...args) => dispatch(action, ...args)
      }
      const chain = middlewares.map(middleware => middleware(middlewareAPI))
      dispatch = compose<typeof dispatch>(...chain)(store.dispatch)

      return {
        ...store,
        dispatch
      }
    }
}

At this part, I understand that store.dispatch is argument as action value of composed middleware.

dispatch = compose<typeof dispatch>(...chain)(store.dispatch)

And the async logic code at Redux official document,

const asyncFunctionMiddleware = storeAPI => next => action => {
  // If the "action" is actually a function instead...
  if (typeof action === 'function') {
    // then call the function and pass `dispatch` and `getState` as arguments
    return action(storeAPI.dispatch, storeAPI.getState)
  }

  // Otherwise, it's a normal action - send it onwards
  return next(action)
}

when action type is function, action excuted as function with storeAPI.dispatch, storeAPI.getState arguments.

I understand the case of async logic part, but I don`t understand when the case of synchronous logic.

If it is not asynchronous processing, I think that store.dispatch should not be given as an argument.

What am I missing?