I see a number of options for sharing maps.
Image
You can as you say create an static image of the map which will work fine in some cases but it really isn't interactive.
Layered PDF
Next step would be to create a layered PDF using the MapInfo PDF Driver where you print to a single file but keep the individual layers as layers in the PDF document.
This adds a small amount of interactivity to the file. The user can turn layers on/off to focus on specific aspects of the map and "ignore" other aspects.
MapInfo ProViewer
MapInfo ProViewer is the free viewer for MapInfo data. Currently it's only available in a 32 bit edition but we are considering how to do this with the 64 bit version. If you have specific thought or questions in relation to this, I'd suggest to reach out to @Jim Stone?.
The latest version of MapInfo ProViewer is 15.0 which can be found here: http://www.pbinsight.com/support/product-downloads/item/mapinfo-proviewer-v15.0
HTML Image Map/MapInfo2Leaflet
These are two MapBasic add-in for MapInfo Pro that can create basic spatial webpages with some sort of interactivity. They are mostly aimed at sharing a single dataset.
Spectrum Spatial Analyst
If you are looking for a full webGIS solution, Spectrum Spatial Analyst is the answer if you ask me. Analyst is a out of the box application for providing webGIS for any organisation.