Mine don't have any pins in them, so I guess it could be a tableball.

Bagatelle, the mother of pinball, was referred to as a table game related to billiards tables. Don't any of you pinheads know your pinball history?

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"It's a coffee table book about pinball tables!"

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Hey kid, remember pinball was prolific in bars and pool halls where we not only put the beer on the pinball tables, we also set our burning cigarettes on the playfield glass. This left behind lovely aromas and character marks for future collectors.

Rotor table games.

http://www.sandsmuseum.com/coinop/games/confuciussay/confuciussay.html

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Learn your pinball history. The origins of pinball begin with the lawn games of Europe, where balls were rolled into holes in the ground. Parlor versions of these games were called “Bagatelle” tables. To play these tabletop games, a stick or plunger would propel ball bearings up an incline. The balls would then roll down the incline, bouncing off pins and landing in pockets labelled with different scoring values. It is these pins that gave pinball its name.

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Nobody will ever win any arguments, people like what they like.

What if you consider individual mechanisms as machines? A pop bumper, a bank of drop targets, etc. - individual machines. Then you could use both terms simultaneously: Its a pinball table full of pinball machines