Guernsey won gold in 2011, the last time table tennis was included in the sports programme for the Island Games.
Alice Loveridge won her women's singles match and teamed up with Dawn Morgan and Garry Dodd for doubles wins.
Dodd beat Bjorn Axelsson 3-1 in the singles, but lost to Nisse Lundberg, who also beat Alex Robinson 3-0 in the opening men's singles match.
Gotland and Guernsey have shared the table tennis gold medals between them for the past decade.
Gotland took gold in 2009, when Guernsey were third, and beat the Sarnians in the 2007 final.
That victory was revenge for the 2005 final, when Guernsey beat the Swedish island.Island hotshots increase medal tally
Jonathan De La Haye won Jersey's seventh shooting gold medal at the 2015 Island Games.
De La Haye took top spot in the men's individual sport trap, beating Dan Bishop of the Isle of Wight by a single point with Guernsey's Andrew Ashplant getting the bronze.
Sarah Campion and Susan De Gruchy won silver in the women's 100 yards prone rifle team event, finishing 15 points behind eventual winners Isle of Man.
Fellow Jersey shooter Caroline De La Haye won bronze in the women's individual sport trap.
Guernsey's Jacek Hanca has won silver in the 50m free pistol, finishing 13 points off Matthew Reed from the Isle of Wight.
Sark celebrated a second shooting medal as Nick Dewe returned to the podium. Dewe, who won team automatic ball trap bronze on Monday, took silver in the individual event.

The draft document now in the public domain had a very limited circulation. Members of Labour's National Executive that I have spoken to hadn't seen it.
Most - though not all - shadow cabinet members were shown only the sections which related to their policy areas - to prevent leaks.
And certainly the leak of a complete version of a draft manifesto before it has been formally discussed is unprecedented.
Sources close to Jeremy Corbyn say "100%" they did not leak it and were shocked around 20:00 BST on Wednesday to find out it had leaked.
And sources close to both the party leader and the Unite leader Len McCluskey are trying to point the finger at the party's deputy leader, Tom Watson.
They say this is all about 9 June. If an impression of chaos around Mr Corbyn is created now, and Labour fails to get 30% of the vote on polling day, it will give his deputy a reason, or excuse, to call for the leader's resignation.
But Mr Watson has categorically denied leaking the manifesto - and his allies say it would have been mad to do so. They see this as an attempt to damage his reputation as he wouldn't want Labour to perform badly at the forthcoming election.
And they say the Labour leader's office had accepted that they hadn't leaked, because the version of the manifesto that Tom Watson had in his possession wasn't the version that made its way to the papers. And sources at the Daily Mirror have made it clear to the BBC that Mr Watson was not the source of the leak.
Other Labour sources are pointing out that union officials saw a draft on Wednesday but Labour now hopes that the debate will move on to substance rather than the internal soap opera.
Guernsey have retained their Island Games team table tennis title after beating Gotland 4-2 in Jersey.
[NEXT_CONCEPT]
It's not just Labour's policies that have been exposed by the leaks of the manifesto - it's the level of distrust at the very top of the Labour Party.