Good Game

Played a pretty good game after a long time. Is this type of ruy lopez good for beginner-skilled players such as mine?

Since you enjoyed this type of position, you might want to play 4.d3 immediately, since 4.0-0 gives Black more options (4...Nxe4 is the main line). After 4.d3 Bc5 5.c3 0-0 6.0-0 d6, you have inserted c3 and prevented Nd4, which is an added bonus. On the 7th move White has a lot of choice (7.Nbd2, 7.h3, 7.Bg5 and 7.Re1 is slightly unusual).

Thanks. What kind of game is this? Are there some terms, like: positional, tactical or other term for this type of game? If there is, I will read about those type of games.
Thanks in advance. :)

It's the Anti-Berlin variation of the Spanish opening (also called Ruy Lopez opening). It's a rare form of "Open Game" (1.e4 e5) that has the characteristics of a closed game : few pieces are exchanged in the first twenty moves, pawns proceed cautiously to the center, tensions are sustained for many moves,...
It's not a sharp game at first, but it can become very tactical when accumulated energy is released by a pawn break in some part of the board. That's a reason why it's played at the highest level : a full array of chess skills are needed to face a GM in this variation. But it's not necessary to be a GM to play it reasonably well, there are thematic plans (c3-b4-a4 for White ; d5 for Black ; kingside operations in certain cases only) and furthermore it is very instructive to develop some experience of this type of position.

You don't need to study a lot of theory to play this. You can also play in the same way against 3...Nf6 4.d3 Be7 (followed by d6) or 3...d6 (the Steinitz Defense) and also against other quiet variations of the Spanish opening (3...Bc5, 3...Nge7, 3...g6, 3...a6 4.Ba4 d6,...). There will be a lot of synergies in your repertoire if you do so. You just need to decide which variation you prefer in the Spanish main line (3...a6 4.Ba4 Nf6 5.0-0 Be7 or Nxe4) and to study a few side lines that are rare but dangerous for the unprepared (3...Nd4, 3...f5,...).
This kind of repertoire is a permanent asset : even if you play something else for 20 years, you can come back to it with some minor updating (you're sure that no such line will ever be refuted).

Short answer to your initial question : yes, it is good for you if you enjoy playing in that way :) .

Thank you sir for such a detailed explanation! :)

Here is an example of how it is played at World Champion level.

Note that white trades off 7 Bxc6 so as to make ...Nd4 impossible.
That trades away white's bad bishop, on the colour of his own pawns d3, e4. You traded away your good bishop 11 Bxf6, which is less smart.

Ok:)