It seems fine. Unless you're looking for a tournament acceptable set, there are specifications for those.
How big chess board?

50 mm is a good size, not too small and not too large. I have a 50 mm board myself. I also have a 55 mm which is the standard tournament size, but these boards can get really big if it has has a broad rim and look "serious".
For normal play I would buy at least a 45 mm, and anything smaller than 40 mm is really small and only good for travelling.
It is a question of personal taste of course, but on the 50 mm board I use only a 3.25" inch chess pieces set. I like if the board has "space" and does not look too dense with the pieces. I like the rule that 4 pawns should be only very slightly larger than the square size. So for the 50 mm board, I would recommend chess pieces where the widest part of the pawn (base) is 26 or 27 mm. And king base approx. 38 mm maximum.

The king height of the set is 97 mm (3.8"), but I don't know any more about it. Here's a picture of the set: http://i.imgur.com/CtSu7lx.jpg
I've also heard about a rule where the bishop should be able to slide between the king and the queen diagonally without touching them.

The king height of the set is 97 mm (3.8"), but I don't know any more about it. Here's a picture of the set: http://i.imgur.com/CtSu7lx.jpg
I've also heard about a rule where the bishop should be able to slide between the king and the queen diagonally without touching them.
It all comes down to what looks good to you but here's a link to some guidelines: http://www.chessusa.com/chess-pieces-size.html

I've also heard about a rule where the bishop should be able to slide between the king and the queen diagonally without touching them.
According to that guideline, you centre the king and queen on diagonally adjacent squares (eg, d4 and e5) and see if the bishop can slide between them.
Another guideline suggests the king's base diameter should be 78 per cent of the width of the square. A 50mm board should be fine with that set; the pieces don't have particularly wide bases.

Mostly a matter of personal taste, but I would say that your set will look cramped on a board w/ 50 mm squares. You should pick one w/ 55mm squares or even 57mm.
As a visual reference you can use for comparison, check this thread:
http://www.chess.com/forum/view/chess-equipment/dubrovnik-1950-reissue?page=2
It shows a set w/ a 89mm King (ie smaller than yours) on three boards, w/ 51 mm, 55mm and 57mm respectively.

> see if the bishop can slide between them
The idea is that king, queen and bishop have the widest bases. If they are able to pass freely diagonally between each other, any piece can.
https://www.youtube.com/watch?v=zJeVid62NZo
-Izmet

The king height of the set is 97 mm (3.8"), but I don't know any more about it. Here's a picture of the set: http://i.imgur.com/CtSu7lx.jpg
I've been looking at the picture. Do you know what square size the board is on which they stand? To my eye, they pieces look slightly too big for those squares. If it's a 50 mm board, I think the pieces would look even better on a 55 mm board.
By the way, I really like the pieces! This German Staunton style is a timeless classic and really perfect for playing and handling. Nothing too fancy or delicate. And nice wood on the dark pieces. I have a very similar set for my 50 mm board.

> see if the bishop can slide between them
The idea is that king, queen and bishop have the widest bases. If they are able to pass freely diagonally between each other, any piece can.
https://www.youtube.com/watch?v=zJeVid62NZo
-Izmet
Yeah, that's where I saw it. Nice video, btw.

The king height of the set is 97 mm (3.8"), but I don't know any more about it. Here's a picture of the set: http://i.imgur.com/CtSu7lx.jpg
I've been looking at the picture. Do you know what square size the board is on which they stand? To my eye, they pieces look slightly too big for those squares. If it's a 50 mm board, I think the pieces would look even better on a 55 mm board.
By the way, I really like the pieces! This German Staunton style is a timeless classic and really perfect for playing and handling. Nothing too fancy or delicate. And nice wood on the dark pieces. I have a very similar set for my 50 mm board.
Yes, the squares are 50 mm. I agree to that they might look a little to big, but I guess it's not too much of a big deal?
And thanks for the compliment.

Definitely not a big deal. The most important thing is that you feel comfortable with your set. That's actually the only thing that matters. Chances are sooner or later you may buy another board, and then you can choose something else (color, size) if you so want.

The idea is that king, queen and bishop have the widest bases. If they are able to pass freely diagonally between each other, any piece can.
I would have thought that, in many Staunton sets, the knight would have a wider base than the bishop.
I use the four pawn test & it has not failed me yet. Place four pawns on a square & they should be slightly under or slightly over the square. Key word is " Slightly ". No board yet? No problem... just draw a square on a piece of paper say 2 1/4 inch square & see how the four pawns fit. If they are under the square quite a bit draw a 2 inch square & see how they fit that square. Good Luck!

I use a guide similar to the four pawns rule. It uses the same principle, that the base of the pawns should be about half the square's width. I set up all of the white pawns on their squares and then fit the black pawns exactly between them. The a and h pawns should still be near the center of their squares (but probably just a little outside of it). If the a and h pawns are too near the edge of the board or touching it, the pieces are too large. If the pawns don't touch each other, the pieces are too small.
I've just bough a chess set over the internet (I live in a small town), but I'm wondering whether 50 mm (2") squares will be too small or not. What size do you guys prefer?