is Excel 2016 Power Pivot work on Excel 2010 by Shared Folder ?

In addition - i'm bit confused with error message you have. If you open in 2010 the file with data model created in 2013/2016 the error shall be like "workbook contains unsupported data model".

If in opposite direction, open in 2013/2016 file with model created in 2010 Excel on initialization phase informs you what data model was created in previous version of Power Pivot and suggests you to upgrade it.

Error message you have looks like related to Power Query connector and means what Excel can't find proper data provider. Anyway, i could be wrong and this error appears first - didn't touch 2010 for a long while. If you load your data into the data model we are in any case have incompatibility issue. If you only connect to Access DB and return the data to Excel tables without using data model that I guess shall work in both versions with proper configuration.